Question

if x3+ax2-bx+10 is divisible by x2-3x+2 .find the value of a and b

Answer 1

since x^2 - 3x + 2 = (x-2)(x-1)
so x^3 + ax^2 -bx + 10 must be divisible by both
x-2 and x-1

let f(x) = x^3 + ax^2- bx + 10
f(2) = 5 + 4a - 2b + 10 = 0 ---> 4a - 2b = -15
f(1) = 1 + a - b + 10 ---> a-b = -11 or a = b-11

sub 2nd into 1st
4(b-11) - 2b = -15
4b - 44 - 2b = -15
2b = 29
b = 29/2
then a = 29/2 - 11 = 7/2

Answer 2

good