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
guapka [62]
2 years ago
15

If (x+2) is a factor of 3x^2-4kx-4k^2, then find the value(s) of k

Mathematics
1 answer:
IRINA_888 [86]2 years ago
4 0

Answer:

The values of k will be:

k=-1,\:k=3

Step-by-step explanation:

Let the expression of polynomial P be

P\left(x\right)=3x^2-4kx-4k^2

Let the expression if the polynomial Q be

\:Q\left(x\right)=\:\left(x+2\right)\:

Plug in Q(x) = 0

0 = x+2

x = -2

As (x+2) is a factor of 3x²-4kx-4k²

substitute x = -2 in the the polynomial

3x²-4kx-4k² = 0

3\left(-2\right)^2-4k\left(-2\right)-4k^2\:=0

12+8k-4k^2=0

Write in the standard form ax²+bx+c = 0

-4k^2+8k+12=0

Factor out common term -4

-4\left(k^2-2k-3\right)=0

Factor k²-2k-3: (k+1)(k-3)

-4\left(k+1\right)\left(k-3\right)=0

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

k+1=0\quad \mathrm{or}\quad \:k-3=0

solving k+1=0

k+1 = 0

k = -1

solving k-3=0

k-3=0

k = 3

Thus, the values of k will be:

k=-1,\:k=3

You might be interested in
What is the result when the number 66 is decreased by 8%?
Andrej [43]

Answer:

60.72

Step-by-step explanation:

Simply if you can, use a calculator and do one of two things. First off, the easier way, you can do 92% of 66, which is 60.72, the more difficult way is to find 8% of 66 which is 5.28, and then subtract 66 by 5.28 which is 60.72. Hope this helps

!

8 0
3 years ago
9a + 18c. What is the value of the expression when a = −5 and c = −1?
saw5 [17]
1. plug in the numbers for the variables, like this: 9(-5)+18(-1)

2. solve
Hopefully this helps! Let me know if you need more explanation.
4 0
3 years ago
Some friends played a board game. During the game, one unlucky player had to move back 8 spaces
podryga [215]
Yes 4+*2 34^%7 shehshshs
6 0
3 years ago
Given that the base of the rock is 14 feet, and the height of the rock is 12 feet, what is the slope on which the vehicle is lea
ExtremeBDS [4]
Hi! So pretty much to find slope of a triangle you are going to use rise/run. The height being 12 and the length is 14. You get 12/14. Simplified is going to be 6/7. :)
4 0
3 years ago
Read 2 more answers
The length of a rectangle is 3 times the width.If the length is decreased by 4 m and the width is increased by 1 m , the perimet
o-na [289]

Answer:

Length = 27 metres

Width = 9 metres

Step-by-step explanation:

Consider the width to be x.

Then the length will be 3x.

The perimeter is 66m when the width is increased by 1m and the length is decreased by 4m.

So the dimensions will become:

Length=3x-4

Width=x+1

Now solve for the variable x using the formula for perimeter of a rectangle:

P = 2(l+b)

66 = 2(3x-4+x+1)     (Divide both sides by 2 and simplify the parentheses)

33 = 4x-3      (Add 3 to both sides)

36 = 4x        (Divide both sides by 4)

x = 9

Now plug-in the value of x into the original dimensions which were:

Length=3x

Width=x

So the dimensions are:

Length = 27 metres

Width = 9 metres

6 0
3 years ago
Other questions:
  • 36 + m = 54<br> 54 - 36 = m<br> 36 + 54 = m<br> 54 / 36 = m<br> 36 x 54 = m
    8·1 answer
  • I need help doing this question
    11·1 answer
  • How do I solve this I don't understand it
    7·1 answer
  • Lyza has a 9 inch board. She wants to measure the length of a small rug in feet. How can she do this?
    7·1 answer
  • The height of a tower is measured as 16.6 m. What is the shortest possible height of the tower?
    5·1 answer
  • Many young black ambitious musicians migrated to Harlem around 1940, where they found an alternative music scene in the after-ho
    13·1 answer
  • How do you factor this trinomial? 2x² + 9x - 18
    5·2 answers
  • I neeed help please i did not understand it
    6·1 answer
  • Hi Guys! Apparently I’m struggling with this hmw and I hope you can help me
    13·1 answer
  • Pat has more than twice as much money as Billy, "b". Pat has $50, how much does Billy have?​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!