Determine the values of k for which the function f(x) = 4x^2-3x + 2kx + 1 has two zeros. Check these values in the original equation.
Answers
k must be greater than or equal to 22.75 to have two different zeros.
How to determine the value of missing coefficient in second order polynomials
Second order polynomials are algebraic expressions that observe the following form:
[tex]p(x) = a\cdot x^2 + b\cdot x + c[/tex] (1)
Where:
a, b, c - Coefficientsx - Independent variableFor polynomials of the form p(x) = 0, we can infer the nature of their roots by applying the following discriminant:
d = b² - 4 · a · c (2)
According to (2), there are three cases:
If d < 0, then there are two conjugated complex roots.If d = 0, then the two roots are the same real number.If d > 0, then the two roots are two distinct real numbers.Now we have the following discriminant case:
-(3 + 2 · k)² - 4 · (1) · (4) ≠ 0
-(9 + 6 · k + 4 · k²) - 16 ≠ 0
-9 - 6 · k - 4 · k² - 16 ≠ 0
4 · k²+ 6 · k +25 ≠ 0
This characteristic polynomial has two conjugated complex roots, then we conclude that all values of k must positive or negative, but never zero. By graphng tools we find that k must be greater than or equal to 22.75 to have two different zeros.
To learn more on polynomials, we kindly invite to check this verified question: https://brainly.com/question/11536910
Related Questions
1. Matthew is at the beach with his family. He is using a rectangular prism-shaped container to mold sand for his sandcastle. The container has the following dimensions: 12 in. by in. by in.
(a) Matthew noticed that the container was one-fourth full of sand. How many more cubic inches of sand would be required to fill the container? Show your work.
(b) Matthew’s father has a container that has dimensions that are each double the dimensions of Matthew’s container. Matthew thought that the volume would also double. Is Matthew correct? How many times greater is the volume of the larger container than the volume of the smaller one? Show your work and explain your reasoning.
2. Jasmine is making a 3-tiered wedding cake. The cake is made up of 3 rectangular prisms.
The bottom tier has a width of 16 in, a length of 16 in, and a height of in. The middle tier has the same height as the bottom tier but has a width and length that are each of the dimensions of the bottom tier. The top tier also has the same height as the bottom tier, but its width and length are each of the dimensions of the middle tier. Jasmine has made enough batter for 2,200 in3 of cake.
Does Jasmine have enough batter to make this cake? Explain and show your work.
3. A rectangular prism has dimensions of , 2, and in.
(a) Determine the edge length of the largest unit cube that you could use to pack the prism. Explain.
(b) What is the volume of the prism? Explain.
(c) How many cubes with the edge length from part (a) will fit into the prism? Explain.
HELPPP!!!ASAP!! K12 PLEASE PLEASE HELP!!!!!!
Answers
Answer:
e
Step-by-step explanation:
cus e duh
What is the length of the triangular prism shown? 25 cm
15 cm
9 cm
25 cm
12 cm the answers are A.86 B.1008 C.1350 D.1080
Answers
To calculate surface area of an object you must calculate the area of each shape land then add them all together.
Answer:
Total Surface Area = 1008 cm^2
Step-by-step explanation:
2 X 1/2 X (12 X 9) (Surface area of the two triangles) (Area of triangle = 1/2 Base X Height)
+ 25 X 15 (Slanted Surface)
+ 25 X 9 (Back Rectangle)
+ 25 X 12 (Bottom Rectangle)
= 1008
please help
me answer this question
Answers
Answer:
x ≥ 4
Step-by-step explanation:
Given:
[tex]\displaystyle \large{3x-1\geq 11}[/tex]
Add both sides by 1:
[tex]\displaystyle \large{3x-1+1\geq 11+1}\\\displaystyle \large{3x\geq 12}[/tex]
Divide both sides by 3:
[tex]\displaystyle \large{\dfrac{3x}{3} \geq \dfrac{12}{3}}\\\displaystyle \large{x\geq 4}[/tex]
Hence, the solution is x ≥ 4
A triangle has an area of 54 m² and a height of 9 m.
How long is the base of the triangle?
Enter your answer in the box.
Answers
Answer:
base = 3
Step-by-step explanation:
The area of triangle is calculated using the following formula:
1/2*b*h (b: base, h: height)
The area and height is given, to find the base we can make the following equation:
1/2*b*9 = 54
9b/2 = 54 multiply both sides by 2
9b = 27 divide both sides by 9
b = 3
Which describes the combined variation in the formula h=2a/b?
h varies jointly with 2 and A and inversely with b.
h varies directly with A and inversely with b.
h varies jointly with A and b.
h varies inversely with A and b.
Answers
Step-by-step explanation:
h varies directly with a and inversely with b.
2 is the constant of variation.
Please Help ASAP (show work if you want its not needed i just need the answer)
Answers
[tex] \sin(60) = \frac{a}{4 \sqrt{3} } \\ [/tex]
[tex] \frac{ \sqrt{3} }{2} = \frac{a}{4 \sqrt{3} } \\ [/tex]
[tex]a = 6[/tex]
_____________________________________________
[tex] \cos(60) = \frac{c}{4 \sqrt{3} } \\ [/tex]
[tex] \frac{1}{2} = \frac{c}{4 \sqrt{3} } \\ [/tex]
[tex]c = 2 \sqrt{3} [/tex]
_____________________________________________
[tex] \sin(45) = \frac{a}{b} \\ [/tex]
[tex] \frac{ \sqrt{2} }{2} = \frac{6}{b } \\ [/tex]
[tex]b = 6 \sqrt{2} [/tex]
_____________________________________________
[tex]d = a = 6[/tex]
Have a great day ♡
(3√7 +5)^2
simplify the problem to its simplest form.
Answers
Answer:
88 + 30[tex]\sqrt{7} \\[/tex]
Step-by-step explanation:
Expand to make easier:
(3[tex]\sqrt{7} \\[/tex] + 5) x (3[tex]\sqrt{7} \\[/tex] + 5)
FOIL:
9(7) + 15 [tex]\sqrt{7}[/tex] + 15[tex]\sqrt{7}[/tex] + 25
Simplify:
63 + 30[tex]\sqrt{7}[/tex] + 25
88 + 30[tex]\sqrt{7}[/tex]
is 1.3 greater than 1.52
Answers
A spinner has 16 equal-sized sections. Twelve of the sections are orange.
a. What is the probability that the spinner will land on orange?
b. Use words to describe the probability
a.
out of 16, or
.
4
b. It is
that the spinner will land on orange.
Answers
The probability that the spinner will land on orange is the likelihhood of landing on orange
The probability that the spinner will land on orange is 0.75
How to determine the probability?From the question, we have:
Spinner section = 16
Orange section = 12
So, the probability that the spinner will land on orange is:
p = 12/16
Evaluate
p = 0.75
Hence, the probability that the spinner will land on orange is 0.75
Read more about probability at:
https://brainly.com/question/251701
how many three-letter "words" can Bob make using just these letters?
Answers
Answer:
two
Step-by-step explanation:
the two "words" Bob can make using the three letters t, o, and a are;
oat and tao
hope this helps
Please help me ASAP
( I will mark brainliest )
Answers
give me brain list please
If Ryan does a job in 10 hours and with the help of Chelsea they can do it together in 5 hours, how long would it take Chelsea to do it alone?
Answers
It would take her 10 hours. If it is double the time for one person to complete the task versus two, you can guess that the other person takes the same amount of time
A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. How many toppings need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same, not including tax?
Answers
Answer:
2 toppings need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same
Step-by-step explanation:
t=toppings
6.80 +0.90t = 7.30+0.65t
0.25t = 0.5
t = 2
-7/3y-2/9=1/3 solve for y
Answers
Answer:
y = -12
Step-by-step explanation:
-7/3y - 2/9 = 1/3
cross multiple for 1/3:
-21/3y - 6/9 = 1
cross multiply for 3y and 9:
-21 - 6 = 3y + 9
3y + 9 = -27
3y = -36
y = -12
5 people are in a line to withdraw money from the local Bank. All 5 withdrawal the same amount. The total withdrawn was $845. How much money did each withdraw? Set up an equation to find out how much money each person withdrew and then solve it.
Answers
845 / 5 = 169
Each person withdrew 169$ from their accounts.
A company interviewed 21 applicants for a recent opening. Of these applicants, 7 wore blue and 6 wore white, while 5 applicants wore both blue and white. What is the number of applicants who wore neither blue nor white?
Answers
Answer:
3 participants
Step-by-step explanation:
7 + 6 + 5 = 18
21 - 18 = 3 participants
1. Tom rides his bike 6_1/4 miles round trip to work. He works 2 days each
week. How far will Tom ride his bike to and from work in 5 weeks?
⚫️31_1/4 miles
⚫️62_1/2 miles
⚫️12_1/2 miles
⚫️62 miles
Answers
Answer:
B. 62 1/2
Step-by-step explanation:
Find the value of x. Round your answer to the nearest tenth.
Answers
Answer:
Value of x is 34.9 (nearest tenth)[tex]~[/tex]
Step-by-step explanation:
In given right angled traingle:
AC (Hypotenuse) = 20∠ACB = 35° AB (Perpendicular) = x[tex]~[/tex]
In ∆ABC,
[tex]\: \: \: \: \dashrightarrow \: \: \: \sf \dfrac {AC}{AB} = \sin35° \\[/tex]
[tex]\: \: \: \: \dashrightarrow \: \: \: \sf \dfrac {20}{x} = 0.5736 \\[/tex]
[tex]\: \: \: \: \dashrightarrow \: \: \: \sf x = \dfrac {20}{0.5736} \\[/tex]
[tex]\: \: \: \:{ \pmb{ \pink{ \sf{ \dashrightarrow \: \: \: { x = 34.867 }}}}}[/tex]
Hence,
Value of x is 34.9 (nearest tenth)awdawddwawwwwwwwwwwwwwwwd dwd awdw w ddw
Answers
Answer:
I'm sorry i dont think i understand what do u need help with
Step-by-step explanation:
Frank is surveying shoppers about their use of the new food court in a mall. Which question in his survey is a statistical question?
How many hours do you spend at the food court each month?
Where is the food court located in the mall?
How many restaurants are there in the food court?
Who is the manager of the food court?
Answers
Answer:
A How many hours do you spend at the food court each month? is a statistical question
Step-by-step explanation:
Because that can have many answers unlike where is the food court in the mall? that question is not statistical because there can only be one answer and so are all the other ones.
Answer:
How many hours do you spend at the food court each month?
Step-by-step explanation:
I just took test got 100% this answer is correct
How many hours do you spend at the food court each month?
hi! i need help finding the area of this shape! thank you
Answers
Answer: 7.5
Step-by-step explanation:
5x3 = 15 A = 1 half L x H
A = (3)(5)
A = 15
A = 15 x 1 half = 7.5
correct me if i am wrong.
how to express 1 cm as a fraction of 1 meter in decimal form
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♫[/tex]
Let's see ~
Remember : value of 1 meter = 100 centimeters
[tex]\qquad \sf \dashrightarrow \:1 \: m = 100 \: cm[/tex]
[tex]\qquad \sf \dashrightarrow \:1 \: cm = \frac{1}{100} \: m[/tex]
[tex]\qquad \sf \dashrightarrow \:1 \: cm = 0.01 \: m[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
As we know
100cm=1mSo
turn down to fraction
[tex]\\ \rm\rightarrowtail \dfrac{1}{100}[/tex]
Turn to decimal
[tex]\\ \rm\rightarrowtail 0.01m[/tex]
simplify the following 72÷6+3×2
Answers
Answer:
18
Step-by-step explanation:
Use PEDMAS
In this, we have to do first division , then multiplication and finally addtion.
72 ÷ 6 + 3*2 = 12 + 3*2 {division is done}
= 12 + 6 {Multiplication is done}
= 18
15x + 2y /= 38
x >/= 0; y>/= 0
Answers
not so sure about the answer
The volume of a cylinder is 81 pi in^3 and the height of the cylinder is 1 in. What is the radius of the cylinder
Answers
Answer:
18/20π
Step-by-step explanation:
81π ÷ 1 = 81π
81π ÷2 = 18/20π
You do this because the radius is half of the diameter and you need to get rid of the hight by dividing it from the volume.
Help help help help help help help
Answers
The answer is 14.
Answer:
14 :)
Step-by-step explanation:
28/2 = 14
Have an amzing day!!
Please rate and mark brainliest!!
Haley has $155 in savings, and her brother Hank has $230. Hayley is saving $10 each week and her brother is spending $15 each week. After how many weeks will their savings account have the same amount of money in them
Answers
Answer:
It will be 3 weeks until their savings account has the same amount of money in them.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
what is 7 times 3 fiths
Answers
Answer:
4-1.5 or 21/5 or 4.2
Step-by-step explanation:
Multiple: 7 * 3/5 = 7 · 3/1 · 5 = 21/5
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(21, 5) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - seven multiplied by three fifths = twenty-one fifths.
.................................................................................................
Answers
Answer:
m<B = 141 degrees
Step-by-step explanation:
This shape is a heptagon meaning its angles should have a sum of 900 degrees.
we are given the degrees and we need to ad them up
148+90+120+129+130+142=749
then we subtract 749 from 900 which looks like
900-749=141
from subtracting 749 from 900 we get 141 hence we get our answer that m<B = 141 degrees
6 - 1 x 0 + 2 ÷ 2
Help meeee
Answers
Answer:
Answer is 1
Step-by-step explanation: 6-1= 5 5x0=0 0+2=2 2 divided by 2 is= 1