1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Varvara68 [4.7K]
3 years ago
14

3. if kx² + 2x + k = -kx have equal roots, find the values of k.​

Mathematics
1 answer:
crimeas [40]3 years ago
5 0

Answer:

k = - \frac{2}{3} , k = 2

Step-by-step explanation:

Using the discriminant Δ = b² - 4ac

The condition for equal roots is b² - 4ac = 0

Given

kx² + 2x + k = - kx ( add kx to both sides )

kx² + 2x + kx + k = 0 , that is

kx² + (2 + k)x + k = 0 ← in standard form

with a = k, b = 2 + k and c = k , thus

(2 + k)² - 4k² = 0 ← expand and simplify left side

4 + 4k + k² - 4k² = 0

- 3k² + 4k + 4 = 0 ( multiply through by - 1 )

3k² - 4k - 4 = 0 ← in standard form

(3k + 2)(k - 2) = 0 ← in factored form

Equate each factor to zero and solve for k

3k + 2 = 0 ⇒ 3k = - 2 ⇒ k = - \frac{2}{3}

k - 2 = 0 ⇒ k = 2

You might be interested in
To make 5 apple pies, you need 2 pounds of apples. How many pounds of apples would you need to make 20 pies?
Dmitrij [34]
10 pounds use division , 20/2=10 pounds of apples total
8 0
3 years ago
Find the percent of decrease from 310 to 140. Round to the nearest tenth of a percent if necessary.
JulijaS [17]
54.8% I think I'm not sure
4 0
2 years ago
12. Find x. (x + 20)° (5x - 8)°​
ololo11 [35]

Answer:

<h2>x = 7</h2>

Step-by-step explanation:

Simplifying

x + 20 = 5x + -8

Reorder the terms:

20 + x = 5x + -8

Reorder the terms:

20 + x = -8 + 5x

Solving

20 + x = -8 + 5x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5x' to each side of the equation.

20 + x + -5x = -8 + 5x + -5x

Combine like terms: x + -5x = -4x

20 + -4x = -8 + 5x + -5x

Combine like terms: 5x + -5x = 0

20 + -4x = -8 + 0

20 + -4x = -8

Add '-20' to each side of the equation.

20 + -20 + -4x = -8 + -20

Combine like terms: 20 + -20 = 0

0 + -4x = -8 + -20

-4x = -8 + -20

Combine like terms: -8 + -20 = -28

-4x = -28

Divide each side by '-4'.

x = 7

Simplifying

x = 7

8 0
3 years ago
Please help! I’ll mark you brainlist
inna [77]

Answer:

B

Step-by-step explanation:

a relation is not a function when input value leads to two or more outputs

5 0
2 years ago
MATHSWATCH
Jobisdone [24]

Answer:19683x

Step-by-step explanation:

Evaluate the exponent

27.93x

27.729x

i am pretty sure sorry if I am wrong

7 0
2 years ago
Other questions:
  • A rocket moves at the speed of 4.9 miles per second. How fast is the rocket traveling kilometers/hour (km/h)? (1 mile = 1.6 kilo
    7·2 answers
  • Haley is making cake for her party. she needs to make 6 servings of cake for every 3 people. if each cake pan contains 12 servin
    9·1 answer
  • A rectangle with an area of 120 in squared has a length of 8 inches longer then two times its width what is the width of the rec
    13·1 answer
  • Find the area of a regular octagon with side length 6 cm
    10·2 answers
  • For the following right triangle, find the side length x
    5·2 answers
  • Explain the steps to solve for g in the equation -1/3g+5=2
    6·2 answers
  • Find the number that belongs in the green box.<br><br>Round your answer to the nearest tenth​
    10·2 answers
  • 4.
    13·1 answer
  • Help please!! I will mark brainilist and give a lot of points.
    11·2 answers
  • Please hurry on an exam The formula for calculating simple interest is I = prt. Which is the equivalent equation solved for r?
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!