Question

If x+1 is a factor of 2x^3+ax^2+2bx+1 and 2a-3b=4, then find the value of a and b.

Answer 1

Solution :

°.° x + 1 is a factor of p ( x ) = 2x^3 + ax^2 + 2bx + 1

Then, by using the factor theorem,

p ( -1 ) = 0

=> -2 + a - 2b + 1 = 0

=> a - 2b = 1 -------------- (equation 1)

Also,

2a - 3b = 4 -------------- (equation 2)

On multiplying equation (1) by 2 and equation (2) by 1, we get

2a - 4b = 2

2a - 3b = 4

- + = -

- b = - 2

.°. b = 2

On putting b = 2 in equation (1), we get

a - 2 × 2 = 1

=> a - 4 = 1

=> a = 1 + 4

=> a = 5

.°. a = 5

Thus,

.°. a = 5 and b = 2.

Answer : a = 5 and b = 2