The equation 12x² + 4kx + 3 = 0 has real and equal roots, if

Answers

Answer 1

Answer:

[tex]k=\pm3[/tex]

Step-by-step explanation:

[...] if you can write the LHS as a perfect square, or if you can't spot a factorization of it right away, if and only if the discriminant [tex]\Delta = b^2-4ac[/tex] (or, if b is an even number, 1/4 of it) is zero.

I see it! I see it!

Stare at it for a while. First term is [tex]3(2x)^2[/tex], third term is [tex]3(1)^2[/tex], we are missing a double product, but we can play with k. For the LHS to be [tex]3(2x\pm1)^2 = 3(4x^2\pm4x+1) = 12x^2\pm12x+3[/tex] you just need [tex]4k= \pm12 \rightarrow k=\pm3[/tex].

I don't see it...

Then number crunching it is. Set the discriminant to 0, solve for k

[tex]\frac{\Delta}4 = 4k^2-12\cdot 3 =0 \rightarrow 4k^2=36 \\k^2 = 9 \rightarrow k=\pm3[/tex]


Related Questions

How to solve quadratic inequalities.

Answers

Find all the zeros of the polynomial, and arrange the zeros in increasing order. ...

Plot those numbers on the number line as open or closed points based upon the original inequality symbol.

Choose a test value in each interval to see if the interval satisfies the inequality or not.

HELP 10 POINTS + BRAINLIEST Determine the equation of the line shown in the graph:
y=0
x=0
y=5
X=5

Answers

Answer:

y=0

Step-by-step explanation:

the x coordinate is 5 and the y coordinate is 0 because the line does not move up the y axis

Answer:

your question is a little messed up.

the equation for the blue line is x = 5

y=x if you're looking for an equation that satisfies (0,0) and (5,5)

The cost of dance lessons is $12 for 1 lesson, $22 for 2 lessons, and $32 for 3 lessons. Use a graph to determine whether the cost is proportional to the number of lessons. Explain your reasoning.

Answers

Answer:

it is not proportional. when you graph it, you will see it is not linear.

Step-by-step explanation:

Answer:

not proportional

Step-by-step explanation:

A graph that’s proportional would have to be linear a straight line but that cannot happen since the numbers are proportional

Its constant of proportionality is 12 and 10 so it could not work.

Simplify x^3 divide by x^2

Answers

The answer would just be x

Juan joins a movie club. He pays $10 to join and each movie costs $5. Which equation represents the relationship between the total cost, y, and the number of movies, x?

Answers

you’re answer is 5x-10=y i think.

find the equation with a diameter that has endpoints located at (2,8) and (2,-4)

Answers

Answer:

32.4/-4.6 nearest circumfrence :)

Step-by-step explanation:

hope that was the method you we're trying to use if not please comment so I can redo it , :) have a great day !

Hailey is putting up a fence in the shape of an isosceles triangle in her

backyard. The fence has side lengths as shown, where x represents the

number of feet in each fence section. The perimeter of the fence can be

covered using 8 total fence sections represented by the expression 8x. If

fencing costs $6.50 a foot, what would be the total cost of the fence?

(2x + 4) ft

(3x + 7) ft

.

(2x + 4) ft

Answers

Answer:

the total cost would be $ 780.00

Step-by-step explanation:

step by step explanation

Solve for b: A = 1 2 (a + b)h.

Answers

Answer:UwU

Step-by-step explanation:

Hello can someone pls help me with this

Answers

Answer:

simple y=5x

Step-by-step explanation:

This is because y and x are the same because anything times 0 is 0 and when x becomes 1, 1*5=5 and that continues the chain

Which relation is a function?

Answers

B. To see if it’s a function, it has to pass the vertical line test. That means draw a vertical line (going up and down) through any point on the graph and it can only go through one point. If it goes through more than 1, it’s not a function. Like in graph A, if you draw a vertical line at x=-2, it will go through two points, same at x=2. For graph b, no matter where you move a vertical line, it only passes through one point at a time, so it passes the vertical line test.

simply the ratio 3:9

Answers

Answer:

1:3

Step-by-step explanation:

The ratio 3:9

3/9=1/3

=1:3

A can of crushed tomatoes holds 40 fluid ounces. How can a label designer name the same volume using metric units? Complete the explanation.

The designer can use the ratio 1 fluid ounce ≈ 29.6 milliliters and then multiply:
40 × blank
=
. The designer might decide to convert mL to L and round to the nearest tenth of a liter:
mL ≈
L

Answers

The metric unit of a quantity is simply the unit of measurement of the quantity

The volumes of the crashed tomato cans are 1184 milliliters and 1.184 liters

The volume of the crushed tomato can is given as:

[tex]\mathbf{Volume = 40oz}[/tex]

From the question, we have the following conversion ratio

[tex]\mathbf{1oz \approx 29.6mL}[/tex]

So, the volume in milliliters becomes

[tex]\mathbf{Volume = 40 \times 29.6mL}[/tex]

Multiply

[tex]\mathbf{Volume = 1184mL}[/tex]

To convert the unit to liters, we simply divide the volume by 1000.

So, we have:

[tex]\mathbf{Volume = 1184L \div 1000}[/tex]

[tex]\mathbf{Volume = 1.184L}[/tex]

Hence, the equivalent volumes are 1184 milliliters and 1.184 liters

Read more about metric units at:

https://brainly.com/question/2004114

Solve for g.

7 − –3g = 13

g =

Answers

Answer: g=2

Step-by-step explanation:

Remove the parentheses

7- (-3)g=13

Move the constant to the right

7+3g=13

Calculate

3g=13-7

Divide both sides

39=6

Answer:

g=2

What value is added to both sides of the equation x^2 − 6x = 10 in order to solve by completing the square? (1 point)

Group of answer choices

−3

3

6

9

Answers

Answer:

9

Step-by-step explanation:

use half the x coefficent and square it

x^2 − 6x + (-3)^2 = 10 + (-3)^2

x^2 - 6x + 9 = 10 + 9

(x - 3)^2 = 19

What dp they mean 2 to the fourth equal 16.

Answers

Answer:

See Below

Step-by-step explanation:

I think you mean 2 the the fourth power, showing 2, with an exponent of 4.

To calculate this, you multiply your base, 2, by itself as many times as the exponent states. Like, 2x2x2x2 because you are multiplying it 4 times by 2.

2x2=4, then 4x2=8, then 8x2= 16.

Hope this helps!

Could someone please help me on this equation?

Answers

Answer:

y = (x+2)x7

Step-by-step explanation:

Answer:

y = 7x + 14

Step-by-step explanation:

1. Add 2 to x = x + 2

2. Multiply x + 2 by 7 = 7(x + 2)

3. Simplify: y = 7x + 14

please i need help i will give 60 point
and show work

Answers

Is it just me or can anyone else not see the picture?

Answer:

1) 1 1/4

2) 1 3/5

3) 1

4) 2 7/8

5) 1 1/8

6) 1/3

7) C

8) B

9) C

10) A

11) B

12) B

Step-by-step explanation:

Hope this helps fr

solve pls brainliest

Answers

Answer:

neither, neither, terminating, repeating

Yeah, I think that the person above is correct

10000+2000003
ghsrhrs

Answers

[tex]⇒10000 + 2000003 = 2010003[/tex]

- BRAINLIEST answerer

Answer: 2010003

Step-by-step explanation: because 10000+2000003= 2010003

24+18a=
help i can not get the answer

Answers

That is the simplest version. Unless you meant 24+18a=0. I assume you meant = 0. So, let’s subtract 24 on both sides. 18a = -24. Then let’s divide by 18 on both sides to get the answer, b = 3/4. Unless you didn’t mean the 0 there, the sneers is in simplest form then.

find two numbers whose sum is 114 and the difference is 58.
(written as an equation please)

Answers

[tex]⇒[/tex]

x + y = 114

x - y = 58

Add the equations downward:

2x + 0y = 172

2x = 172

x = 86

x + y = 114

86 + y = 114

y = 114 - 86

y = 28

Answer: The two numbers are 28 and 86.

Please mark me brainliest

Find the slope of the line x=+6

Answers

Step-by-step explanation:

x = 6

is a straight vertical line (parallel to the y-axis, going through x=6 on the x-axis).

it's slope is therefore undefined (infinite). every possible y value (from -infinity to +infinity) is associated with this one x value (6).

Of the 345 7th graders, 40% of them
are in band. How many 7 graders
are in band?

Answers

So first you find 10% which is 34.5
Then you multiply 10% by 4 to get 40% which is = 138

So first you find 10% which is 34.5

Then you multiply 10% by 4 to get 40% which is = 138s

Yw

your amazing and beautiful or handsome or whatever you are comfortable with!:D​

Answers

Answer:

1. C

2. E

3. D

4. A

5. B

Step-by-step explanation:

1. It shows that the number of students decrease.

2. It increases more than the breakfast (B)

3. It's on thin line representing the students and workers whom stayed in the cafeteria.

4. It increases showing the same amount of students that entered the other day.

5. The same

What number has 62 hundreds and 5 tens

Answers

Answer:

6250

Step-by-step explanation:

62 hundreds is the same as 62 X 100 which equals 6200.

5 tens is the same as 5 X 10 which equals 50.

And if we add these together, we get a total of 6250

write an equation in
Slope-int form
m=9, b=4

Answers

Answer:

y=9x+4

Step-by-step explanation:

9 is the slope and 4 is the y-intercept, or the "b"

Billy and Michael have 2 lemonade stands. Billy charges $2 per lemonade plus a flat rate of $2.
Michael charges $3 per lemonade plus a flat rate of $1.

How many lemonades would they have to sell to be making the same amount of money?

Answers

1 lemonade.

2x+2=3x+1

-x+2=1
-x=-1
x=1 lemonade

The length of a rectangle is five centimeters less than width. Find the dimensions of the
rectangle if its area is 50 cm?

Answers

Answer:

w is 10 and l is 5

Step-by-step explanation:

l=w-5

lw=50

w^2-5w-50=(w-10)(w+5) since the negative solution does not make sense w=10 and therefore l is 5 so the length is 5 while the width is 10

(Pythagorean theorem) find the missing side length. Round to the nearest hundredth (show steps)

Answers

Answer:

The missing length is 10.44

Step-by-step explanation:

a^2 + b^2 = c^2

3^2 + 10^2 = c^2

9 + 100 = c^2

109 = c^2

√c^2 = √109

c = √109

c ≈ 10.440307

c ≈ 10.44

Answer:

10.44

Step-by-step explanation:

Pythagorean theorem equation is a²+b²=c²

3²+10²=c²

9+100=c²........simplify

109=c².............add

√109=c

10.44031

10.44................round to the nearest hundredth

i will put brailly helpppppppppppppppppppppppppppppppppppppppppp

Answers

Answer:

1. Even Chance

2. Even Chance

3. No Chance

4. No Chance

5. Even Chance

(NOT SURE)

(but im sure)

Other Questions
question 8 what does the following expression equal when y = 32 x (y - 5) workout the perimeter of this shape 3cm 5cm 2cm 6cm According to the concept of tragic hero, can we consider the happy prince and the swallow tragic heroes? Pleaseeee help me!!!! How to integrate absolute value. Please help asap thank you!! if f(x)=3x+7, find: f(-2)= [?] pllz answer Masterson Wood Products pays Patricia Griffin a $640 monthly salary plus a 11% commission on merchandise she sells each month. Assume Patricia's sales were $72,900 for last month. 9. Circle the element in each pair that has the greater electronegativity. Ca or Ge Li or o CI or s Br or As How did the study of the atom contribute to our understanding of the periodic table of the elements? (1 point) Atoms are representative of elements, so scientists scaled up O atomic char- derstand elemental characteristics, allowing sc Highlight e elements in a periodic table. The determination of electron charge led to an understanding of O how atoms interact with one another, which facilitated the organization of the periodic table. Elements are made of atoms, so understanding atoms provided O information about elements, which led to the organization of the periodic table. Experiments that identified characteristics of atoms provided O scientists with atomic weights and atomic numbers, which were used to organize the periodic table. a result of freedom summer campaign was that The comparative financial statements of marshall inc. Are as follows. The market price of marshall common stock was $82. 60 on december 31, 20y2. Some researchers argue that the robust australopiths should be classified in a separate genus. What is that genus called please no links i just need help The area of the triangle is less than 18 square inches. Select an inequality that represents a Whats that answer please The educational issues facing the United States in the early 2000s include a. Educational reform. C. Free trade. B. Political disagreement. D. All of the above Please select the best answer from the choices provided A B C D. While screening and evaluating ideas, a stop-to-market mistake happens when ________. Multiple Choice a 10kg model rocket is fired at a 60 degree angle from horizontal from the football field with a thrust of 200N. what is the acceleration of the rocket? If you had taken the PSAT test can you tell me if it is hard, what topic is on it (especially math) and what happens basically?I got an email saying it was for 8/9 grade and I'm in 8th. It is free for me and I'm wondering what I have to do. Do I need to make an account on psat.org or will my teacher send me a link to the test?