The real roots of the equation x^2 + 5|x| + 4 | vedclass

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(D) Given equation: $x^2 + 5|x| + 4 = 0$. Since $x^2 = |x|^2$,the equation becomes $|x|^2 + 5|x| + 4 = 0$. Let $t = |x|$,where $t \ge 0$. The equation

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$D) 	ext{None of these}$

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(D) Given equation: $x^2 + 5|x| + 4 = 0$. Since $x^2 = |x|^2$,the equation becomes $|x|^2 + 5|x| + 4 = 0$. Let $t = |x|$,where $t \ge 0$. The equation is $t^2 + 5t + 4 = 0$. Factoring the quadratic: $(t + 1)(t + 4) = 0$. This gives $t = -1$ or $t = -4$. Since $|x| = t$ and the absolute value must be non-negative $(|x| \ge 0)$,there are no real values of $x$ that satisfy $|x| = -1$ or $|x| = -4$. Therefore,the equation has no real roots.

The real roots of the equation $x^2 + 5|x| + 4 = 0$ are

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