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Question -

If x = 0 and x = -1 are the roots of the polynomial f(x) = 2x3 – 3x2 + ax + b, find the value of a and b.



Answer -

f(x) = 2x3 – 3x2 + ax + b
∵ x = 0and x = -1 are its zeros
∴ f(0) =0 and f(-1) = 0
Now, f(0) = 0
⇒ 2(0)3 – 3(0)2 + a x 0 + b = 0
⇒ 0-0 +0 + b= 0
∴ b = 0
and f(-1) = 0
⇒ 2(-1)3 –3(-1)2 + a(-1) + b = 0
⇒ 2 x (-1) – 3 x 1 + a x (-1) + b = 0
⇒ -2-3-a + b = 0
⇒ -2-3-a+ 0 = 0
⇒ -5- a= 0=>a =-5
Hence a = -5, b = 0

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