1.

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

Answer»

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 


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