Question

If 0 and 1 are the zeroes of the polynomial f (x) = 2x3 – 3x2 + ax + b, then find the
values of a and b.​

Answer 1

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It is given that both 0 and 1 are the zeroes of the polynomial f(x) = 2x^3 - 3x^2 + ax + b, so numeric value of the polynomial should be 0 on substituting the numeric value of zeroes.

Therefore, f(0) = 0
= > 2(0)^3 - 3(0)^2 + a(0) + b = 0
= > 2(0) - 3(0) + a(0) + b = 0
= > b = 0

Hence the required value of b is 0
When x = 1, f(1) = 0
= > 2(1)^3 - 3(1)^2 + a(1) + b = 0
= > 2(1) - 3(1) + a( 1 ) + 0 = 0 {b=0}
= > 2 - 3 + a = 0
= > - 1 + a = 0
= > a = 1
Hence, a = 1 & b = 0