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Zeroes of a Polynomial

The zeroes of...

Question

The zeroes of square of polynomial $x^{2} + 5 x + 6$ are ______ .

A

-2 & -3

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B

4 & 9

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C

-4 & -9

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D

2 & 3

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Solution

The correct option is A -2 & -3
Given, $x^{2} + 5 x + 6$
Lets factorise before squaring.
$x^{2} + 5 x + 6$ $= x^{2} + 3 x + 2 x + 6 x (x + 3) + 2 (x + 3) (x + 2) (x + 3)$

Squaring: $x^{2} + 5 x + 6$
$(x^{2} + 5 x + 6)^{2}$ $= {[(x + 2) (x + 3)]}^{2} = (x + 2)^{2} (x + 3)^{2}$

Lets find zeroes,
$(x + 2)^{2} = 0; (x + 3)^{2} = 0$
Take square root on both side.
$x + 2 = 0; x + 3 = 0 x = - 2; - 3$

Zeroes are -2 and -3.

Conclusion: Roots of the equation will be same.
$x^{2} + 5 x + 6 = (x + 2) (x + 3)$
Zeroes are $x = - 2; - 3$

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