Form the quadratic equation with rational coefficients whose one of the root is:
$3 - 2 \sqrt{3}$

x^{2} - 3 x - 6 = 0

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x^{2} + 6 x - 3 = 0

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x^{2} + 3 x - 6 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{2} - 6 x - 3 = 0

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Solution

The correct option is D $x^{2} - 6 x - 3 = 0$
If one of the roots of the equation is $3 - 2 \sqrt{3}$ other will be $3 + 2 \sqrt{3}$
Thus, sum of roots $= 6$
Product of roots $= (3 - 2 \sqrt{3}) (3 + 2 \sqrt{3})$ = $9 - 4 \times 3 = - 3$
Hence, the equation can be written as $x^{2} - S x + P = 0$
$∴ x^{2} - 6 x - 3 = 0$

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