Question

If the gcd of x2-px-4 and x2+2x+(p-2) is x+1, then the value of p is:

Answer 1

Answer:

value of p=3.

Step-by-step explanation:

" gcd of two polynomials means that it is a common factor of both the polynomials ".

Here we are given $gcd=x+1$

this means that $(x+1)$ is a factor of both the polynomials.

i.e.

$x= -1$ is a zero of both the polynomial.

This implies on putting $x=-1$ in polynomial equation $x^2-px-4$

we have polynomial equation will be equal to zero.

$x^2-px-4=0$  at $x=-1$

$1-(-1)p-4=0\\\\1+p-4=0\\\\p-3=0\\\\p=3$

similarly on putting $x=-1$ in second polynomial and equating it equal to zero we will have $p=3$

Hence, the value of p=3.