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Question

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


A
(1,4)
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B
(1,4)
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C
(4,4)
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D
No real root
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Solution

The correct option is D No real root
Given equation
$$x^2 + 5|x| + 4 = 0 $$
$$\Rightarrow |x|^2 + 5|x| + 4 = 0$$
Put $$|x|=t$$
$$\Rightarrow t^2+5t+4=0$$
$$\Rightarrow (t + 1) (t + 4) = 0$$
$$\Rightarrow t=-1,-4$$
$$|x| = -1, |x| = -4$$
Both are not possible .
Hence, no real roots .

Mathematics

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