Question

Find the value of p and q so that x^4 + px^3+2x^2-3x+q is divisible by x^2-1.

Answer 1

If x^4+px^3+2x^2-3x+q is divisible by x^2 - 1, then it is divisible by x - 1 and x + 1,

Therefore f(1) = f(-1) = 0

That is

f(1) = 1 + p + 2 - 3 + q = 0

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

f(-1) = 1 - p + 2 + 3 + q = 0

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

Solving (1) and (2)

q = -3 and p = 3

Answer 2

Answer:

The value of p and q are 3 and -3 respectively.

Step-by-step explanation:

It is given that $x^4+px^3+2x^2-3x+q$ is divisible by $x^2-1$, then it is divisible by x - 1 and x + 1,  

Therefore f(1) = f(-1) = 0 ,That is  

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

⇒$p+q=0$                           (1)

Also, $f(-1)=1-p+2+3+q=0$

⇒$-p+q=-6$                         (2)

Now, solving the equations (1) and (2), we get

$2q=-6$

⇒$q=-3$

Substituting the value of q in equation (1), we get

$p-3=0$

⇒$p=3$

Thus, the value of p and q are 3 and -3 respectively.