Quadratic polynomial having sum of its zeroes 5 and product of its zeroes -14 is _________.

x^{2} - 5 x - 14

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x^{2} - 10 x - 14

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x^{2} - 5 x + 14

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x^{2} - 10 x + 14

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Solution

The correct option is C $x^{2} - 5 x - 14$
Consider, the roots of a quadratic polynomial as $a$ and $b$ .
Then the quadratic polynomial with the zeroes as $a$ and $b$ is $x^{2} - (a + b) x + a b$ .
Here, $a + b = 5$ and $a b = - 14$ .
Therefore the quadratic polynomial formed from the following roots is $x^{2} - 5 x - 14$ .
Therefore,Option A is correct.

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