Question

If (x + 1) is a factor of 2x³ + ax² + 2bx + 1, then find the values of a and b given that 2a - 3b = 4.

• A. a = 2, b = 2
• B. a = 2, b = 5
• C. a = 5, b = 2
• D. a = 5, b = 5

Answer 1

The correct option is C

a = 5, b = 2

Since, (x + 1) is a factor of f(x) = 2x³ + ax² + 2bx + 1,

f(-1) = 0

-2 + a - 2b + 1 =0

a - 2b = 1 ...(1)

Given, 2a - 3b = 4 ...(2)

Solving (1) and (2), we get,

a = 5

b = 2