Question

If x³ + x² – ax + b is divisible by (x² – x), write the values of a and b.

Answer 1

Equating x² – x to 0 to find the zeroes, we will get

x(x – 1) = 0

⇒ x = 0 or x – 1 = 0

⇒ x = 0 or x = 1

Since, x³ + x² – ax + b is divisible by x² – x.

Hence, the zeroes of x² – x will satisfy x³ + x² – ax + b

∴ (0)³ + 0² – a(0) + b = 0

⇒ b = 0

And (1)³ + 1² – a(1) + 0 = 0   ...[∵ b = 0]

⇒ a = 2