Find a quadratic polynomial each with the given numbers as the zeroes of the polynomial.
$2 \sqrt{3}, - 2 \sqrt{3}$

x^{2} + 12

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x^{2} + 2 x - 12

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x^{2} - 2 x + 12

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x^{2} - 12

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Solution

The correct option is D $x^{2} - 12$
Given roots: $2 \sqrt{3}, - 2 \sqrt{3}$

Sum of the roots= $2 \sqrt{3} + (- 2 \sqrt{3})$
= $0$

Product of the roots= $(2 \sqrt{3}) (- 2 \sqrt{3})$
= $- 4 (3)$
= $- 12$

Now, the quadratic equation is given by,
$x^{2} -$ (sum of roots) $x +$ (product of the roots)
$= x^{2} - (0) x + (- 12)$

$= x^{2} - 12$

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