Question

If (x-1) is a factor of p(x)=x2+x+k , then find the value of k

Answer 1

x-1= 0 = 1
x2+ x+ k
By putting the value of x-1=0= 1 in polynomial.
1^2 +1 +k =0
1+1+k =0
2+k=0
K=-2 ans.

Answer 2

Given:

If (x-1) is a factor of p(x)=x2+x+k

To Find:

find the value of k

Solution:

It is given that (x-1) is a factor of p(x)=x2+x+k and we need to find the value of k, first, we should know what a factor has properties in the case of polynomial, which can be understood by Remainder theorem,

According to the Remainder theorem, a polynomial P(x) when divided by a linear equation of the form x-a then P(a) would give the remainder of the given polynomial.

So if (x-1) is the factor of the given polynomial then P(1) will result in the polynomial value of 0.

So putting P(1)=0 and finding the value of k,

[tex]P(x)=x^2+x+k\\ P(1)=1^2+1+k\\ k+2=0\\ k=-2[/tex]

Hence, the value of k is -2.