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If 2 and $- \frac{1}{2}$ is the sum and product of the zeroes of the polynomials respectively then the quadratic polynomial f(x) is

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x^{2} - 2 x - 4

4 x^{2} + 2 x + 1

2 x^{2} + 4 x - 1

2 x^{2} - 4 x - 1

answer is D.

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Detailed Solution

Given, 2 and

- \frac{1}{2}

is the sum and product of the zeroes of the polynomials.
We need to find the quadratic polynomial f(x).
Let us assume

α

β

be the zeroes of the quadratic polynomial

a x^{2} + bx + c

, then

(α + β) = 2 = - \frac{b}{a},

αβ = - \frac{1}{2} = \frac{c}{a}

a = 2

, then

b = - 4

, and

c = - 1 .

Then, the required polynomial will be

2 x^{2} - 4 x - 1

.
Hence, the correct option is 4.

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