Q24 of 109 Page 3

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


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