Question

for what value of k,(x+1) is a factor of p(x)=kx2-x-4

Answer 1

Hey there!!

Given that (x+1) is a factor og p(x) so by factor theorem p(-1) = 0

=> k(-1)^2 -(-1) - 4 =0

=> k + 1 -4 = 0

=> k = 3

___________________,,,,,,,,,,

Hooe it will help u

Answer 2

Given,

A function, p(x)=k$x^{2} -x-4$. . .(1)

(x+1) is a factor of p(x).

To Find,

Value of K.

Solution,

We know that the factor theorem is that if P(x) is a polynomial,p$x^{2} +qx+r$

If (x+a) be a factor of this polynomial, then P(-a) will be 0.

So here as (x+1) is a factor of p(x), then p(-1)=0.

Now put x=0 -1 in (1), we get

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

⇒k-3=0.

⇒k=3.

Hence, the value of k is 3.