Question

If 2 and 0 are zeros of polynomial f(x) =2x³-5x²+ax+b then find the value of a and b
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Answer 1

Answer:

a = 2; b = 0

Step-by-step explanation:

$f(x) = 2x^3 - 5x^2 + ab + b\\\\\\\text{Given zeroes: 2, 0}\\\\\\f(2) = 2(2)^3 - 5(2)^2 + a(2) + b\\\\\\= 2(8) - 5(4) + 2a + b\\\\\\= 16 - 20 + 2a + b\\\\\\= 2a + b - 4\\\\\\\text{Since 2 is a zero of f(x), f(2) = 0.}\\\\\\\implies 2a + b - 4 = 0\\\\\\\implies 2a + b = 4 --- \text{eqn.1}\\\\\\\text{Similarly, f(0) = 0}\\\\\\\implies 2(0)^3 - 5(0)^2 + a(0) + b = 0\\\\\\\implies b = 0 --- \text{eqn.2}\\\\\\\text{From eqn.1 and eqn.2, we get}\\\\\\2a = 4\\\\\implies a=2$

Therefore, a = 2; b = 0.

Answer 2

Answer:

The value of a=2

And the value of b=0