Find an equation whose roots are negative of the roots of $x^{2} + 5 x + 6 = 0$

x^{2} - 3 x + 2 = 0

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x^{2} + 6 x - 5 = 0

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x^{2} - 5 x + 6 = 0

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None of the above

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Solution

The correct option is D $x^{2} - 5 x + 6 = 0$
We know, to find an equation whose roots are negative of the roots of the given equation, we simply replace $x$ with $- x$ in the given equation.
So in the given equation, $x^{2} + 5 x + 6 = 0$
$\Rightarrow (- x)^{2} + 5 (- x) + 6 = 0$
so the required equation is: $x^{2} - 5 x + 6 = 0$

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