The equation whose roots are the square of the roots of $x^{2} + 4 x + 5 = 0$ is

x^{2} - 6 x + 25 = 0

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x^{2} + 10 x + 25 = 0

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x^{2} + 6 x + 25 = 0

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x^{2} - 26 x + 25 = 0

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Solution

The correct option is A $x^{2} - 6 x + 25 = 0$
Let $α, β$ be the roots of $f (x) = x^{2} + 4 x + 5 = 0$
Thus, equation whose root are $α^{2}, β^{2}$ is,
$f (\sqrt{x}) = 0 \Rightarrow (\sqrt{x})^{2} + 4 \sqrt{x} + 5 = 0$
$\Rightarrow x + 5 = - 4 \sqrt{x}$
Squaring on both sides
$\Rightarrow (x + 5)^{2} = (4 \sqrt{x})^{2}$
$\Rightarrow x^{2} + 10 x + 25 = 16 x$
$\Rightarrow x^{2} - 6 x + 25 = 0$

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