Question

Determine the values of a and b if (x-3) is a factor of x3 + ax2 + bx – 9 and when it is divided by(x-2) , the remainder is 1.​

Answer 1

Answer :

a = -13/2

b = 27/2

Solution :

Given,

(x-3) is the factor of x³ + ax² + bx - 9

x = 3

(3)³ + a(3)² + b(3) - 9 = 0

18 + 9a + 3b = 0

b + 3a = -6 ━━━━━━━━ equation 1

When (x-2) is divided, the remainder is 1.

x = 2

(2)³ + a(2)² + b(2) - 9 = 0

4a + 2b = 1

b + 2a = 1/2 ━━━━━━━━ equation 2

Subtract eq 2 from 1

b + 3a - (b + 2a) = -6 - 1/2

a = -13/2

From equation 2,

b - 13 = 1/2

b = 27/2

Hope it helps...