Question

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

plzzzzzz answer its urgent

Answer 1

Given polynomial,

x⁴+px³+2x²+3x+q

x²-1 divides the given polynomial.

Then x²-1=0

x² = 1

x = √1

x = ±1

Put x=1,

(1)⁴+p(1)³+2(1)²+3(1)+q = 0

1+p+2+3+q = 0

p+q+6 = 0

p+q = -6 -----(1)

Put x= -1,

(-1)⁴+p(-1)³+2(-1)²+3(-1)+q = 0

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

1-p-1+q = 0

-p+q = 0 --------(2)

(1)+(2)

p+q = -6
-p+q = 0
-------------
2q = -6

q = -6/2

q = -3

p+q = -6

p+(-3)=-6

p-3=-6

p = -6+3

p = -3

Therefore, p = q = -3

Hope it helps