If f(x) = x3 + x2 – ax + b is divisible by x2 – x write the values of a and b.
a = 2, b = 0
Given,
A polynomial f(x) = x3 + x2 – ax + b
Which is divisible by x2 – x
Now,
x2 – x = (x – 1) = (x – 0)(x – 1)
(x – 0) and (x – 1) are factors of polynomial f(x)
⇒ f(0) = 0
⇒ 03 + 0 – a × 0 + b = 0
⇒ b = 0
And f(1)
13 + 1 – a × 1 + b = 0
⇒ 2 – a = 0
⇒ a = 2
∴ a = 2 and b = 0