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 options are
C
-3

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

Given that $x - \sqrt{5}$ is a factor of the cubic polynomial $x^{3} - 3 \sqrt{5} x^{2} + 13 x - 3 \sqrt{5}$ find all the zeroes of the polynomial.

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

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

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

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

x - \sqrt{5}

x^{3} - 3 \sqrt{5} x^{2} - 5 x + 15 \sqrt{5}