Question

if the GCD of x2+(p-1) and x2-px+(p-1) is x-1,then the value of p is?​

Answer 1

Answer:

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Answer 2

The correct question is:

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

Given:

Given two numbers are: x²-px-4 and x²+2x+(p-2).

To Find:

We have to find the value of p.

Solution:

We all know that the 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 x² - px - 4

we have polynomial equation will be = zero.

x² - px - 4 = 0 at x = -1

⇒ 1 - (-1)p - 4 = 0

⇒ 1 + p - 4 = 0

⇒ p = 3

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

Hence, the value of p=3.