The sum and product of zeros of the quadratic polynomial are - 5 and 3 respectively the quadratic polynomial is equal to

x^{2} + 2 x + 3

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x^{2} - 5 x + 3

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x^{2} + 5 x + 3

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x^{2} + 3 x - 5

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Solution

The correct option is C $x^{2} + 5 x + 3$
If $α$ , $β$ be the zeros of the quadratic polynomial ,then
$(x - α) (x - β)$ is the quadratic polynomial.
Thus, $(x - α) (x - β)$ is the polynomial.
$= x^{2} - α x - β x + α β$
$= x^{2} - x (α + β) + α β (i)$
$(α + β) = - 5 α β = 3$
Now putting the value of $(α + β), α β$ in equation (i) we get,
$x^{2} - x (- 5) + 3$
$= x^{2} + 5 x + 3$

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Similar questions

A quadratic polynomial whose zeros are $5$ and $- 3,$ is

(a) $x^{2} + 2 x - 15$

(b) $x^{2} - 2 x + 15$

(d) none of these

What should be added to the quadratic polynomial x²-5x+4 so that 3 is a zero of the resulting polynomial ?

x^{2} - 4 x + 3

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