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guapka [62]
3 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]3 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

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