Question

find the value of k , if x+k is factor of the polynomial -4x³+4x²+4kx-k

Answer 1

Solution :

Let p(x) = -4x³+4x²+4kx-k

if x + k is a factor of p(x)

then

p(-k) = 0

=> -4(-k)³+4(-k)²+4k(-k)-k=0

=> 4k³+4k²-4k²-k = 0

=> 4k³ - k = 0

=> k(4k²-1)=0

=>k[(2k)²-1²]=0

=> k(2k+1)(2k-1)=0

=> k = 0 or 2k+1 = 0 or 2k-1=0

=>k=0 or k = -1/2 or k = 1/2

••••