Given that - 4 is a root of the equation $2 x^{3} + 6 x^{2} + 7 x + 60 = 0$ . Find the other roots.

$\frac{1 \pm i \sqrt{29}}{2}$

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$\frac{1 \pm i 5}{2}$

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$\frac{1 \pm i \sqrt{2}}{2}$

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$\frac{2 \pm 5 i}{2}$

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Solution

The correct option is A
$\frac{1 \pm i \sqrt{29}}{2}$

Given that -4 is a root of the given equation. This implies that (x + 4) is a factor of $2 x^{3} + 6 x^{2} + 7 x + 60 = 0$

It dividends $2 x^{3} + 6 x + 7 x + 60$ with zero remainder

$\begin{matrix} 2 x^{2} - 2 x + 15 x + 4 & 2 x^{3} + 6 x^{2} + 7 x + 50 - 2 x^{3} - 8 x^{2} - 2 x^{2} + 7 x + 60 - 2 x^{2} - 8 x 15 x + 60 - 15 x - 60 0 \end{matrix}$

Quotient is $2 x^{2} - 2 x + 15 = 0$

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} = \frac{2 \pm \sqrt{4 - 120}}{4} = \frac{1 \pm i \sqrt{29}}{2}$

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Similar questions

Given that - 4 is a root of the equation $2 x^{3} + 6 x^{2} + 7 x + 60 = 0$ . Find the other roots.

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