Question

find value of k is x+1 is factor of p(x)=x^2-kx+5k​

Answer 1

Given :

x+1 is factor of p(x)= x^2-kx+5k

To find :

Value of k

Solution :

We can easily solve this mathematical problem by using the

following process.

According to the question, x+1 is a factor of the polynomial p(x)= x^2-kx+5k

Therefore the value of p(x) will be zero for x= -1.

So, substituting x= -1 in the given polynomial, we get

  (-1)²-k*(-1)+5k

= 1+k+5k

= 1+6k

Now, with respect to the to the aforesaid explanation,

1+6k = 0

Therefore, 6k = -1

therefore, k = $\frac{-1}{6}$

Hence, the value of k is $\frac{-1}{6}$