Question

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Find the values of p and q ​

Answer 1

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+qx

4

+px

3

+2x

2

−3x+q is divisible by x^2-1x

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=0f(1)=1+p+2−3+q=0

⇒p+q=0p+q=0 (1)

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

⇒-p+q=-6−p+q=−6 (2)

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

2q=-62q=−6

⇒q=-3q=−3

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

p-3=0p−3=0

⇒p=3p=3

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

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