Question

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

Answer 1

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Answer 2

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

answer : a = 1 and b = 0

explanation : 0 and 1 are the zeros of the polynomial f(x) = 2x³ - 3x² + ax + b.

so, f(0) = 0 and f(1) = 0

now, f(0) = 2(0)³ - 3(0)² + a(0) + b = 0

⇒0 - 0 + 0 + b = 0

⇒b = 0.......(1)

again, f(1) = 2(1)³ - 3(1)² + a(1) + b = 0

⇒2 - 3 + a + b = 0

⇒a + b - 1 = 0

⇒a + b = 1 ........(2)

from equations (1) and (2),

a = 1 .

hence, value of a = 1 and b = 0