Question

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

Answer 1

Heyya Mate,

Answer with Explanation...

Let 0 and 1 be the zeroes of polynomial f(x) = $2x^{2} - 3x^{2} + ax + b$

then, f(0) = 0 as well as f(1) = 0

now,

$f(0) = 2 (0)^{2} - 3(0)^{2} + a(0) + b$

$f(0) = 2*0 - 3*0 + 0 +b$

$f(0) = 0 - 0 + 0 +b$

$f(0) = b = 0$                 ...........................(1)

and,

$f(1) = 2(1)^{2} - 3(1)^2 + a(1) + b$

$f(1) = 2 * 1 - 3 * 1 + a + b$

$f(1) = 2 - 3 + a + b$

$f(1) = (-1) + a + b = 0$

$f(1) = (-1) + a = 0$                       ..............from (1) [(b = 0)]

$f(1) = a = 1$

Thus,

a=1

b=0

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