If sum of the roots is $2$ and product is $5$ , then the quadratic equation is

x^{2} + 2 x + 5 = 0

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x^{2} - 2 x - 5 = 0

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x^{2} + 2 x - 5 = 0

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x^{2} - 2 x + 5 = 0

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Solution

The correct option is C $x^{2} - 2 x + 5 = 0$
Given the sum of the roots is 2 and the product of the roots is 5.
Therefore, the quadratic equation is given by $x^{2} -$ (Sum of the roots) $x +$ (Product of the roots) $= 0$ .
$∴ x^{2} - 2 x + 5 = 0$ is the quadratic equation.

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If the sum of the roots of a quadratic equation is 5 and the product of the roots is also 5, then the equation can be $x^{2} - 5 x + 5 = 0$ .

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