If `x^3+a x^2-b x+10` is divisible by `x^2-3x+2,` find the values of `a` and `b`

Explanation

1409719 `x^3+ax^2-bx+10` is divisible by `x^2-3x+2`
Factors of `x^2–3x+2` are `(x-1) (x-2)`
`f(1)=0`
`=>1+a-b+10=0`
`=>a-b=-11`..........(i)
`f(2)=0`
`2^3+2^2a-2b+10=0`
`8+4a-2b=-10`
`=>4a-2b=-18`
`=>2a-b=-9`..........(ii)
Subtracting equation (i) and equation (ii):
`a-2a-b+b=-11+9`
`=>-a=-2`
`=>a=2`
From equation(1):
`a-b=-11`
`2-b=-11`
`2+11=b`
`b=13`
`therefore` The value of `a=2` and `b=13`.