Find a quadratic polynomial, the sum and product of whose zeroes are respectively :

$- 11 a n d 10$

x^{2} + x + 5

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x^{2} + 11 x + 10

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x^{2} + x - 5

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x^{3} + 11 x + 10

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Solution

The correct option is A $x^{2} + 11 x + 10$
Let the quadratic polynomial be $a x^{2} + b x + c$ and its zeros be $α$ , $β$

We know that,
$α + β = \frac{- b}{a} = \frac{- (- 11)}{1}$
$α \times β = \frac{c}{a} = \frac{10}{1}$
If, $a = 1$ , $b = 11$ , $c = 10$
Therefore,
The quadratic equation which fits the condition is $x^{2} + 11 x + 10$

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