The real roots of the equation {x^2} + 5|x| + | 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: $|x|^2 + 5|x| + 4 = 0$.Let $|x| = t$,where $t \ge

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

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

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