Question

If f(x) = x³ + x² − ax + b is divisible by x² − x write the value of a and b.

Answer 1

We are given f(x) = x³ + x² − ax + b  is exactly divisible by  x² − x then the remainder should be zero

Therefore Quotient  = x+2 and

Remainder `= x(2 -a)+ b`

Now, Remainder  = 0 

`x (2 - a)+ b = 0`

`x ( 2 - a) + b = 0 x + 0 `

Equating coefficient of x, we get

`2 - a = 0 `

` 2 = a`

Equating constant term

b = 0 

Hence, the value of a and b are  ` a= 2 , b = 0 `