Q15 of 113 Page 61

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


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