If one root of a quadratic equation is 1 1 + 3 , then the quadratic equation is

Question

If one root of a quadratic equation is $\frac{1}{1 + \sqrt{3}},$ then the quadratic equation is

Smart Achievers · Accepted Answer

(4)

$One root = \frac{1}{1 + \sqrt{3}} = \frac{1 - \sqrt{3}}{- 2} = - \frac{1}{2} + \frac{\sqrt{3}}{2}$

$∴$ $Other root = - \frac{1}{2} - \frac{\sqrt{3}}{2}$

$Sum = - 1, product = \frac{1}{4} - \frac{3}{4} = - \frac{1}{2}$

$∴$ $Required equation is x^{2} + x - \frac{1}{2} = 0$

$or$ $2 x^{2} + 2 x - 1 = 0$

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