Question

find a and b if x3-ax3-13x-b has x2+2x-3 as a factor

Answer 1

Answer:

Let p(x) = x3 – ax2 – 13x + b be the given polynomial.

If (x – 1) and (x + 3) are the factors of p(x) then

p(1) = 0

and p(-3) = 0

p(1) = (1)3 – a(1)2 – 13(1) + b = 0

= 1 – a – 13 + b = 0

a – b = -12

p(-3) = (- 3)3 – a(- 3)2 - 13(- 3) + b = 0

= - 27 – 9a + 39 + b = 0

9a – b = 12 ….(2)

Solving (1) and (2) we get

a = 3

and b = 15