Find all the common zeroes of the polynomials $x^{3} + 5 x^{2} - 9 x - 45$ and $x^{3} + 8 x^{2} + 15 x$ .

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-3

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-5

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Solution

The correct option is D
-5

Let $p (x) = x^{3} + 5 x^{2} - 9 x - 45$
$q (x) = x^{3} + 8 x^{2} + 15 x$

$p (x) = x^{3} + 5 x^{2} - 9 x - 45$

$p (x) = x^{2} (x + 5) - 9 (x + 5)$

$p (x) = (x + 5) (x^{2} - 9)$

$p (x) = (x + 5) (x + 3) (x - 3)$

$\Rightarrow$ Zeroes are -5,-3 and 3.

$q (x) = x^{3} + 8 x^{2} + 15 x$

$q (x) = x (x^{2} + 8 x + 15)$

$q (x) = x (x + 5) (x + 3)$

$\Rightarrow$ Zeroes are 0, -5 and -3

Therefore, common zeroes are -5 and -3.

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Similar questions

The common zeroes of the polynomials $x^{3} + 5 x^{2} - 9 x - 45$ and $x^{3} + 8 x^{2} + 15 x$ are:

x^{3} + 5 x^{2} - 9 x - 45

x^{3} + 8 x^{2} + 15 x

x^{3} - 8 x^{2} + 5 x + 50

Find all the common zeroes of the polynomials x^3+5x^2-9x-45 and x^3+8x^2+15x

Plz do it step by step. . Like all the divisions and plz divide it in a befitting manner

x^{3} - 3 x^{2} - 9 x - 5

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