Find a quadratic equation each with the given numbers as the sum and product of its zeroes respectively.
$2 \sqrt{3} - 1, 3 - \sqrt{3}$

x^{2} - (2 \sqrt{5} - 1) x + (3 - \sqrt{3})

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x^{2} - (2 \sqrt{1} 1 - 1) x + (3 - \sqrt{3})

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x^{2} - (2 \sqrt{3} - 1) x + (3 - \sqrt{3})

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x^{2} - (2 \sqrt{7} - 1) x + (3 - \sqrt{3})

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Solution

The correct option is D $x^{2} - (2 \sqrt{3} - 1) x + (3 - \sqrt{3})$
Given:
Sum of the roots= $2 \sqrt{3} - 1$
Product of the roots= $3 - \sqrt{3}$
Now,the quadratic equation is given by,
$x^{2} -$ (sum of roots) $x +$ (product of the roots)
$= x^{2} - (2 \sqrt{3} - 1) x + (3 - \sqrt{3})$

The above equation is the required quadratic equation.

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