Form the quadratic equation with rational coefficients, if its one of the root is
$2 + \sqrt{5}$ , then the equation is

2 x^{2} - 4 x - 1 = 0

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x^{2} - 2 x - 1 = 0

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x^{2} - 4 x - 1 = 0

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x^{2} - 4 x - 2 = 0

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Solution

The correct option is C $x^{2} - 4 x - 1 = 0$
If one root is $2 + \sqrt{5}$ then the other root will be $2 - \sqrt{5}$
Sum of root = $4$
Product of roots = $(2 + \sqrt{5}) (2 - \sqrt{5})$ = 4 - 5 = -1

The equation whose standard form is $x^{2} - S x + P = 0$ will be, $x^{2} - 4 x - 1 = 0$

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