Question

For which value of K, - 4 is a zeroes of polynomial x²-x-(2K+2)

Answer 1

Let the polynomial be p(x)

We have,

p(x)=x²-x-(2k+2)

Given that -4 is a zero of above p(x)

Thus,

p(x) = p(-4)=0

Now,

p(-4)=(-4)²-(-4)-(2k+2)

→0=16+4-2-2k

→2k=18

→k=9

For k=9,-4 is a factor of given polynomial