Question

if x² + x + 1 is a factor of x4 + px³ + qx² - 1 , then find value of p and q .

please solve it .

thanku..

Answer 1

Answer:

Step-by-step explanation:

Answer:

value of p = 3 and q = -3.

Step-by-step explanation:

Given polynomial,

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)

p(-1) = 0

....................(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.