If x3 + x2 ‒ ax + b is divisible by (x2 ‒ x), write the values of a and b.
Firstly, equating x2 – x to 0 to find the zeros we get:
x (x – 1) = 0
x = 0 or x – 1 = 0
x = 0 or x = 1
As x3 + x2 – ax + b is divisible by x2 – x
∴ The zeros o x2 – x will satisfy x3 + x2 – ax + b
Hence, (0)3 + 02 – a (0) + b = 0
b = 0
Also,
(1)3 + 12 – a (1) + 0 = 0
∴ a = 2