Find a quadratic equation each with the given numbers as the sum and product of its zeroes respectively.

$\frac{- 10}{\sqrt{3}}, 7$

3 x^{2} - 11 \sqrt{3} x + 21 = 0

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3 x^{2} - 17 \sqrt{2} x + 21 = 0

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3 x^{2} + 10 \sqrt{3} x + 21 = 0

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3 x^{2} - 15 x + 21 = 0

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Solution

The correct option is C $3 x^{2} + 10 \sqrt{3} x + 21 = 0$
Given:
Sum of the roots= $\frac{- 10}{\sqrt{3}}$

Product of the roots $= 7$

Now,the quadratic equation is given by,

$x^{2} -$ (sum of roots) $x +$ (product of the roots) $=$ 0

$= x^{2} - (\frac{- 10}{\sqrt{3}}) x + (7)$ $=$ 0

$= x^{2} + \frac{10 \sqrt{3}}{\sqrt{3} \times \sqrt{3}} x + 7$ $=$ 0

$= x^{2} + \frac{10 \sqrt{3}}{3} x + 7$ $=$ 0

$= \frac{1}{3} (3 x^{2} + 10 \sqrt{3} x + 21)$ $=$ 0

$= (3 x^{2} + 10 \sqrt{3} x + 21)$ $=$ 0

The above equation is the required quadratic equation.

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