Question

Find the values of p and q so that x+1 and x-1 are the factors of x4 + px3 + 2x2 - 3x + q

Answer 1

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Answer 2

Answer:

value of p = 3 and q = -3.

Step-by-step explanation:

Given polynomial, $p(x)=x^4+px^3+2x^2-3x+q$

Factors of p(x) are x + 1  & x - 1

According to factor theorem which states that a linear polynomial of form x - a is factor of polynomial p(x) if p(a) = 0

So, we get

p(1) = 0

$1^4+p(1)^3+2(1)^2-3(1)+q=0$

$1+p+2-3+q=0$

$p+q=0$ .............(1)

p(-1) = 0

$(-1)^4+p(-1)^3+2(-1)^2-3(-1)+q=0$

$1-p+2+3+q=0$

$q-p=-6$ ....................(2)

Add eqn (1) & (2) we get

2q = - 6   ⇒ q = -3

put this in eqn(1)

p + (-3) = 0 ⇒ p = 3

Therefore, value of p = 3 and q = -3.