Question

given that x+2 and x+3 are factors of 2x³+ax²+7x-b. determine values of a and b.

Answer 1

Answer:

If x + 2 is a factor of 2x3 + ax2 + 7x – b, then x + 2 = 0 x = - 2 in equation

2(- 2)3 + a(- 2)2 + 7(- 2) – b = 0

2(- 8) + a(4) + 7(- 2) – b = 0

-16 + 4a – 14 – b = 0

4a – b = 30 …(1)

Also given that x + 3 is a factor of

2x3 + ax2 + 7x – b, then x + 3 = 0

x = - 3 in equation

2(- 3)3 + a(- 3)2 + 7(- 3) – b = 0

2(- 27) + a(9) + 7(- 3) – b = 0

- 54 + 9a – 21 – b = 0

9a – b = 75 ….(2)

Solving (1) and (2), we get

a = 9, b = 6