What are the real roots of the equation x^2 + | vedclass

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(D) Given the equation: $x^2 + 5|x| + 4 = 0$. Since $x^2 = |x|^2$,we can rewrite the equation as: $|x|^2 + 5|x| + 4 = 0$. Factoring the quadratic expr

Vedclass · Accepted Answer

No real roots exist.

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(D) Given the equation: $x^2 + 5|x| + 4 = 0$. Since $x^2 = |x|^2$,we can rewrite the equation as: $|x|^2 + 5|x| + 4 = 0$. Factoring the quadratic expression in terms of $|x|$: $(|x| + 1)(|x| + 4) = 0$. This gives two possibilities: $|x| = -1$ or $|x| = -4$. Since the absolute value $|x|$ must always be non-negative $(|x| \ge 0)$,neither $|x| = -1$ nor $|x| = -4$ is possible. Therefore,there are no real roots for the given equation.

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

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