First slide

Theory of equations

Question

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

Moderate

A

$- 1, - 4$
B

$1, 4$
C

$- 4, 4$
D

none of these

Solution

Clearly, $x^{2} + 5 | x | + 4 > 0$ for all $x \in R$ .
Therefore, $x^{2} + 5 | x | + 4 = 0$ has no real roots.

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