Question

If x3 + ax2 – bx + 10 is divisible by x2 – 3x + 2, find the values of a and b.

Answer 1

Answer:

a = 2 and b = 13

Step-by-step explanation:

Fractorising x2 – 3x + 2

x² - 2x - x +2=0

x(x-2)-1(x-2) =0

x = 1 or 2

Hence if x3 + ax2 – bx + 10 is divisible by x2 – 3x + 2, then it should satisfy x = 1 and 2..

Substituting for x we get,

x = 1 or 2 in x3 + ax2 – bx + 10

1³ + a1² - b1 + 10=0 or 2³ + a2² - b2 +10=0

a-b = -11 or 4a - 2b = - 18 ( 2a - b = -9)

a - b = - 11

2a-b = -9

-

_________

-a = -2

a = 2 and b = 13