Question

Find the value of k,if x+k is factor of polynomial p(x)= -4x^3+4x^2+4kx-k​

Answer 1

Answer:

4k^3

Step-by-step explanation:

p(x) -4x^3+4x^2+4kx-k

p(-k) = -4(-k)^3 + 4(-k)^2 + 4k(-k) -k

4k^3+ 4k^2 - 4k^2 - k

4k^3- k

p(-k)=0

4k^3-k=0

4k^3=k

Answer 2

Values of k is $0,+\frac{1}{2} ,-\frac{1}{2}$

Step-by-step explanation:

Given,

(x + k) is a factor of  $p(x) = -4x^{3} + 4x^{2} +4kx-k$

( x + k ) is a factor of p(x), therefore p(-k) will be equal to 0

∴ $p(-k) = -4(-k)^{3} + 4(-k)^{2} +4k(-k)-k$

Solving the above equation we get ,

$p(-k) = 4k^{3} + 4k^{2} - 4k^{2} -k$

$p(-k) = 4k^{3} -k$

As we know that p(-k) = 0,

∴ $4k^{3} -k = 0$

$k(4k^{2} -1) = 0$

$k = 0 \\4k^{2} -1 = 0$

∴ k =0 or $4k^{2} =1$

k =0 or k = ±  $\frac{1}{2}$

Hence the values of k is $0,+\frac{1}{2} ,-\frac{1}{2}$