. If a, b, c are real numbers such that ac # 0
then show that at least one of the equations
ax + bx+ c=0 and -ax + bx+ c=0 has real
roots.

Answers

Answer 1

Answer:

  if one equation has no real roots, the other must have real roots. Hence, at least one equation has real roots.

Step-by-step explanation:

The discriminant of the first equation is ...

  d1 = b^2 -4ac

The discriminant of the second equation is ...

  d2 = b^2 +4ac

__

Suppose the first equation has no real roots. Then ...

  d1 < 0

  b^2 -4ac < 0

  b^2 < 4ac

We know that b^2 is non-negative, so this means 4ac is positive. For that case,

  d2 = b^2 +4ac

is the sum of a positive number and a non-negative number so will be positive. When the discriminant is positive, there are two real roots.

When the first equation has no real roots, the second one must have two real roots.

__

Suppose the second equation has no real roots. Then ...

  d2 < 0

  b^2 +4ac < 0

  b^2 < -4ac

Again, b^2 is non-negative, so -4ac must be positive. For this case, the sum ...

  d1 = b^2 -4ac

is the sum of a non-negative and a positive number, so will be positive. The positive discriminant means there are two real roots.

When the second equation has no real roots, the first one must have two real roots.

One of these equations will have real roots, or not. If not, the other must have (distinct) real roots.


Related Questions

The central angle of sector R is 38° and the central angle of sector Q is 39°. What is the probability that the spinner does not land on Q or R? P Q R S T U

Answers

Answer: 0.786

Step-by-step explanation:

Here i would assume that:

Sector R and Sector Q do not have any sections in common.

Then, the probability that the spinner does not land on Q or R, is equal to the probability where the spinner does not land in a specified section of:

38° + 39° = 77°.

Now, the total section off the spinner is 360°.

If we remove those 77°, we have a section of:

360° - 77° = 283°

So we have 283° where the spinner CAN land on.

Then the probability that the spinner does NOT land on R or Q is equal to the quotient between the section of the spinner that is not R or Q, and the total section of the spinner"

P = 283/360 = 0.786

So the probability is 0.786

I need help. I don’t understand what I have to do

Answers

Answer:

Hey there!

3x-5+2x+2+3x+5

3x+2x+3x-5+2+5

8x+2=90

8x=88

x=11

Let me know if this helps :)

Step-by-step explanation:

Hey, there!!

Let's simply work with it,

MA is perpendicular to AT.

To find: angle HAT.

Now,

angle HAT + (2x + 2)° + (3x + 5)° = 90° { As MA perpendicular to AT. }

Now,

Replace angle HAT by (3x - 5)°.

(3x-5)° + (2x+2)° + (3x+5)° = 90°

Open brackets,

3x - 5° + 2x + 2° + 3x + 5° = 90°

Add like terms.

8x + 2°= 90°

8x = 90°-2°

[tex]x = \frac{88°}{8} [/tex]

x= 11°.

Now, finding the value of angle HAT.

(3x-5)° = 3×11°-5°

Therefore, angle HAT is 28°.

Hope it helps...

If the discriminant of a quadratic equation is 4 which statement describes the roots.

Answers

Answer:

2 real roots

Step-by-step explanation:

If the discriminant is >0 then the equation has 2 real roots

If the discriminant is =0 then the equation has 1 real roots

If the discriminant is <0 then the equation has 2 complex roots

since the discriminant is 4, it has 2 real roots

Answer:

It will have 2 real roots

Step-by-step explanation:

4>0 :)

What is the actual distance of 9 cm on a map whose scale shows that 3 cm = 5 km? A. 18 km incorrect answer B. 12 km incorrect answer C. 21 km incorrect answer D. 15 km

Answers

Answer:

15 km

Step-by-step explanation:

3 cm on the map = 5 km

3 x 3 = 9 cm

5 x 3 = 15 km

So, 9 cm on the map = 15 km

Answer:

D. 15 km

Step-by-step explanation:



​please help me!!!!!

Answers

Answer: 194

Step-by-step explanation:

1. Square both sides to get (b+2)=14^2=196

2. Subtract 2 from both sides to get b=194

please help me on this !

Answers

Answer:

B.) 20

Step-by-step explanation:

We know the midpoint of half of the segment, which is 5. You can use this to find the length of half, after which you can find the entire length by multiplying by 2:

[tex]RN+NS=RS\\5+5=10\\HR+RS=HS\\10+10=20[/tex]

The length of HS is 20.

7is subtracted from the quotient of 48 divided by th
e sum of 5 & difference of 11 and 8​

Answers

Answer:

7-48=41

÷

5+11-8

bodmas

5+3=8

41÷8=5.125

Answer:

-1

Step-by-step explanation:

48/(5+(11-8) -7

48/(5+3) -7

48/8 -7

6-7

-1

i hope it helped you. i tried you help you

The measures of two angles of a triangle are 49° and 75°. Find the measure of the third angle in degrees.

Answers

Answer: 56 degrees


Step by step:
The three angles in a triangle add up to 180 degrees.
49 + 75 + the third angle = 180
Let’s simplify.
180 - 49 - 75 = the third angle
So, by subtracting, we know that the third angle is 56 degrees!


Hope this helps! Please tell me if I did anything wrong, thank you so much and have a good day!

Which statement about the stamps is correct?

Karl has stamps in his desk drawer. The possible

combinations of stamps are shown below.

Karl's Stamp Collection

The total number of stamps is 25.

The total value of the stamps is $18.75.

The total number of stamps is 35.

The total value of the stamps is $19.15.

Number of

Number of

45-cent stamps 65-cent stamps

18

17

2015

22

13

10

25

Answers

Answer: C.) The total number of stamps is 35.

Step-by-step explanation:

Given the table :

No of 45-cent stamp - - - No of 65-cent stamp

- - - - - - - 18 - - - - - - - - - - - - - - 17

- - - - - - - 20 - - - - - - - - - - - - - - - 15

- - - - - - 22 - - - - - - - - - - - - - - 13

- - - - - - 10 - - - - - - - - - - - - - - - - 25

Verifying each option stated :

Total value of stamp:

Each row add up to 35. Example (18 + 17) = 35

(20 + 15) = 35

(22 + 13) =35

(10 + 25) = 35

Total value of stamp:

Using the first row:

45 cent = $0.45 ; 65 cent = $0.65

(10 * 0.45) + (25 * 0.65)

= $4.5 + $16.25 = $20.75

Not all rows add up to $19.15

Answer:

Your answer is C

Step-by-step explanation:

the density of concentrated sulphuric acid is 1.8 g/cm.calculate the volume of 3.1 kg of the acid​

Answers

Step-by-step explanation:

[tex]density = \frac{mass}{volume} \\ volume = \frac{mass}{density} \\ changing \: 1.8 {gcm}^{ - 3} to \: {kgm}^{ - 3} \\ multiply \: by \: 1000 \\ = 1800 {kgm}^{ - 3} \\ volume = \frac{3.1}{1800} \\ = 0.00172 {m}^{ 3} [/tex]

The volume of 3.1 kg of concentrated sulfuric acid is 1722.22 [tex]cm^{3}[/tex].

Here's the solution:

The density of concentrated sulfuric acid is 1.8 g/[tex]cm^{3}[/tex]. This means that 1.8 grams of concentrated sulfuric acid will occupy 1 cubic centimeter of space.

If we have 3.1 kg of concentrated sulfuric acid, then we have 3100 grams of concentrated sulfuric acid.

The volume of this amount of concentrated sulfuric acid will be:

volume = mass / density

volume = 3100 g / 1.8 g/[tex]cm^{3}[/tex]

volume = 1722.22 [tex]cm^{3}[/tex]

Therefore, the volume of 3.1 kg of concentrated sulfuric acid is 1722.2[tex]cm^{3}[/tex]

Learn more about volume here: brainly.com/question/28058531

#SPJ2

The graph below is a portion of the complete graph. On a separate sheet of paper sketch the complete graph assuming it is symmetric with respect to the x-axis. Then list 3 points from the new part of the graph that you sketched.

Answers

Answer:

(-1, -3), (-2, -5), (-5, -8),(-8, -5), (-9, -3)

Step-by-step explanation:

These are the options of points to pic from. :)

have a good day.



You have to catch the bus at 11:15am for a movie! It
takes you twenty minutes to shower and dress, fifteen minutes to eat breakfast, and ten
minutes to walk to the bus stop. By what time should you get you get up?

Answers

Answer:

Hey there!

To solve this problem, we must first find the total amount of time it takes for you to get ready in the morning!

20 minutes for shower + 15 minutes to eat + 10 minutes to walk.

This is a total of 20+15+10 or 45 minutes.

For our answer, we have that you should wake up 45 minutes before 11:15, which is 10:30 AM.

Let me know if this helps :)

Answer:

10:30 am

Step-by-step explanation:

11:15 am - 20 min = 10:55 am10:55 am - 15 = 10:40 am10:40 am - 10 = 10:30 am

I hope this helps!

At a corner bakery, 6 croissants and 3 cups of coffee costs $25.95. An order of croissants and 6 cups of coffee costs $26.70. What is the cost of an order of 1 croissants and 1 cup of coffee?

Answers

Answer:

$6.36

Step-by-step explanation:

this is a system of equations problem. There are two main methods for this type of problem: elimination and substitution(I used both here). A-croissants, B-coffee.

The cost of an order of 1 croissant is $2.3 and 1 cup of coffee is $4.05.

We need to form the system of equations for the given statement.

What is the system of equations?

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Let the cost of croissants be x and the cost of cups of coffee be y.

6 croissants and 3 cups of coffee costs $25.95

6x+3y=25.95-----(1)

1 croissant and 6 cups of coffee cost $26.70

x+6y=26.70-----(2)

(6x+3y)6=25.95×6

⇒36x+18y=155.7-----(3)

(x+6y)3=26.70×3

⇒3x+18y=80.1-----(4)

Subtract (4) from (3).

That is, 36x+18y-(3x+18y)=155.7-80.1

⇒33x=75.6

⇒x=2.3

Substitute x=2.3 in equation (1).

That is, 6(2.3)+3y=25.95

⇒3y=12.15

⇒y=4.05

Therefore, the cost of an order of 1 croissant is $2.3 and 1 cup of coffee is $4.05.

To learn more about the system of equations visit:

https://brainly.com/question/21620502.

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When converting θ = π/3 to a Cartesian equation, let x = ____
1/2 r
√2/2 r
√3/2 r

Answers

The equations

[tex]x = r*\cos(\theta)\\\\y = r*\sin(\theta)[/tex]

are useful to convert from polar to Cartesian

So,

[tex]x = r*\cos(\theta)\\\\x = r*\cos\left(\frac{\pi}{3}\right)\\\\x = r*\frac{1}{2} \ \text{ use unit circle} \\\\x = \frac{1}{2}r[/tex]

Answer: Choice A

Given: 5x – 21 = 24
Prove: X = 9
list the statements

Answers

Proof:
5x-21=24
5x=24+21
5x=45
x=9

Hope this can help.

Stacy milk to make pancake batter. The recipe calls for 3/4 of jug of She 1/4 a jug How much more milk does she need?

Answers

Answer:

More milk does she need = 1 / 2 jug

Step-by-step explanation:

Given:

Recipe call milk = 3/4 jug

Stacy had = 1/4 jug

Find:

More milk does she need

Computation:

More milk does she need = 3/4 - 1/4

More milk does she need = (3 - 1) / 4

More milk does she need = 2 / 4

More milk does she need = 1 / 2 jug

A is the midpoint of LB, LB = 6x - 17 and AB = 2x + 3

Answers

6x - 17 = 2(2x + 3) since AB is half of what LB is. Therefore AB would have to be doubled to make them equal. Then 6x - 17 = 4x + 6 by distribution, and 2x - 17 = 6 by subtraction, and 2x = 23. So x = 11.5

I would appreciate some help :)

Answers

Answer:

See below

Step-by-step explanation:

(a) Remember that the median of any data set is represented by the " middle line " of the box plot. The median of Brand X would be 13, and the median of Brand Y would be 16.

(b) The median of each respective box plot is not in range of their respective boxes. Therefore Brand X has a much smaller time span that Brand Y. This proves that one would favor Brand Y over Brand X.

To estimate the percentage of defects in a recent manufacturing​ batch, a quality control manager at selects every th that comes off the assembly line starting with the until she obtains a sample of . What type of sampling is​ used? A. Systematic B. Stratified C. Convenience D. Simple random E. Cluster

Answers

Answer: systemic

Step-by-step explanation:

Select the correct answer.
Which expression simplifies to 2V15?
O A. 17
19
V30
D. V60

HELP!! im doing the plato test rn​

Answers

Answer:

D

Step-by-step explanation:

Prime factorize 60

[tex]\sqrt{60}=\sqrt{2*2*3*5}=2\sqrt{3*5}=2\sqrt{15}[/tex]

what is 7/2 as a mixed number ​

Answers

Hello! :)

Answer:

[tex]\huge\boxed{3\frac{1}{2}}[/tex]

[tex]\frac{7}{2}[/tex] as a mixed number:

Divide 2 from 7 and find the remainder:

7 ÷ 2 = 3 R 1.

An improper fraction in mixed form has the quotient as the coefficient, and the remainder over the fraction. Therefore:

[tex]\frac{7}{2} = 3\frac{1}{2}[/tex]

Answer:

[tex]3\frac{1}{2}[/tex]

Step-by-step explanation:

Step 1: Define mixed fraction

A mixed fraction is a number with a whole number and a fraction together

Step 2: Find mixed fraction

Ask how many time can 2 completely fit into 7 without leaving anything left over, 2 fits in 7 3 times because 2 x 3 = 6 and 7 - 6 is 1.  We put 3 in front of the fraction and we keep the 1 left over in the numerator of the fraction with 2 as the denominator to get [tex]3\frac{1}{2}[/tex]

The upper-left coordinates on a rectangle are (-5, 6)(−5,6)left parenthesis, minus, 5, comma, 6, right parenthesis, and the upper-right coordinates are (-2, 6)(−2,6)left parenthesis, minus, 2, comma, 6, right parenthesis. The rectangle has a perimeter of 16units.

Answers

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

The upper-left coordinates on a rectangle are (−5,6) and the upper-right coordinates are (−2,6). The rectangle has a perimeter of 16units. Draw the rectangle on the coordinate plane below.

If the coordinates of the top of the triangle (breadth) is  (−5,6) and  (−2,6), we can calculate the breadth of the rectangle by taking the difference between the two points using the formula:

D = √(y₂-y₁)²+(x₂-x₁)²

Given x₁ = -5, y₁= 6, x₂ = -2 and y₂ = 6

D = √(6-6)²+(-2-(-5))²

D = √0²+3²

D = √9

D = 3 units

Breadth = 3 units

Given the Perimeter to be 16 units and the formula for calculating the perimeter of rectangle t be P = 2(L+B), we can get the length of the rectangle.

16 = 2(3+L)

16 = 6+2L

16-6 = 2L

2L = 10

L = 10/2

L = 5 units.

Hence the length of the rectangle is 5 units and the breadth is 3 units. Find the diagram in the attachment.

Answer:

This other person is correct! I checked =)

Step-by-step explanation:

The parabola $y = ax^2 + bx + c$ is graphed below. Find $a+b+c$. (The grid lines are one unit apart.)

Answers

If [tex]x=0[/tex], then [tex]y=a\cdot0^2+b\cdot0+c=5[/tex], so [tex]c=5[/tex].

If [tex]x=1[/tex], then [tex]y=a\cdot1^2+b\cdot1+c=2[/tex], so [tex]a+b+5=2[/tex] or [tex]a+b=-3[/tex].

If [tex]x=2[/tex], then [tex]y=a\cdot2^2+b\cdot2+c=1[/tex], so [tex]4a+2b+5=1[/tex] or [tex]2a+b=-2[/tex].

We have

[tex]a+b=-3\implies -a-b=3[/tex]

[tex](2a+b)+(-a-b)=-2+3[/tex]

[tex]\implies a=1\implies b=-4[/tex]

So we end up with

[tex]a+b+c=1+(-4)+5=\boxed{2}[/tex]

In the equation 18/2 = 9, nine is the:

Answers

Answer:

Quotient.

Step-by-step explanation:

You get a quotient by dividing something. It is the end result, the solution.

Answer: quotient

Step-by-step explanation: The answer to a division

problem is called the quotient.

So here we say the quotient of 18/2 is 9.

Valerie is the building manager for the cowardly enterprise office building One of her responsibilities is cleaning the office buildings 200 gallon aquarium for cleaning she must remove the fish from the aquarium in drain the water the water drain a constant rate of 10 gallons per minute what is the independent and dependent variables

Answers

Answer:

The independent variable = The volume of water in the aquarium

The dependent variable = The time it will take to drain the aquarium

Step-by-step explanation:

The independent variable, as indicated in the name is the variable that is not influenced by other variables but can predetermine its own self and it is not altered by the other variables being analysed

Therefore, the independent variable is the water in the 200 gallon aquarium

The dependent variable, is the tested or measured variable and is dependent on the independent variable, which is the time it takes to drain the 200 gallon aquarium.

Ali's heart beats 320 times in 4 minutes. How many beats per minute is that?

Answers

Answer:

90 beats per minute

Step-by-step explanation:

320 divided by 4 is 90, which would mean that there is 90 beats per minute

Answer: the answer is 64 beats.

Step-by-step explanation:

When bisecting a line segment, why must you find the intersection points of the arcs both above and below the line segment?
(1 point
The intersection point above the line segment overestimates the midpoint, while the intersection point below the line segment
underestimates the midpoint
Only one intersection point is needed to find the midpoint, but finding both points allows you to check your work
Finding both intersection points helps if the line segment is not completely vertical or horizontal
Ite
To make sure that you get a straight ine to bisect the line segment

Answers

Answer:

To make sure that you get a straight line to bisect the line segment

Step-by-step explanation:

Answer:

The last option.

Step-by-step explanation:

You get a straight line that passes through the midpoint.

please help me out!
simplify:
|-5| + 2

Answers

Answer:

7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Recall that absolute value is the positive of a real number so

|-5| = 5

This added to 2 gives 7

3x=9 divide each side by 3 x=3

Answers

Answer:

3

Step-by-step explanation:

3x=9

3(3)=9

3/3=0=9/3=3

answer=3

-8 + 10 + (-3) -(-2)

Answers

Answer:

1

Step-by-step explanation:

-8 + 10 + (-3) - (-2)

=> -8 + 10 - 3 + 2

=> 12 - 11

=> 1

Answer:

1

Step-by-step explanation:

[tex]-8+10+\left(-3\right)-\left(-2\right)\\\\Follow\:the\:PEMDAS\:order\:of\:operations\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:\:\\\\-8+10=2\\\\=2+\left(-3\right)-\left(-2\right)\\\\\mathrm{Apply\:rule\:}+\left(-a\right)\:=\:-a\\\\+\left(-3\right)=-3\\\\=2-3-\left(-2\right)\\\\2-3=-1\\\\=-1-\left(-2\right)\\\\=-1+2\\\\=1[/tex]

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