Question

If x3-10x2+ax+b is divided by (x-1)&(x-2) then find the value of a&b

Answer 1

x³ - 10x² + ax + b = 0

x - 1 =0; x = 1                                       x - 2 = 0; x  = 2

1 - 10 + a + b =0                                     8 - 40 -2a + b = 0

a + b - 9 = 0                                           -2a + b - 32 = 0

(a + b - 9 - ( -2a + b - 32) = 0

3b = - 23

b = -23/3

a + b = 9

a + - 23/3 = 9

a = 9 + 23/3 = 50/3