For the equation $x^2-5|x|-14=0$

For the equation $x^2-5|x|-14=0$
  1. all roots are real
  2. all the roots are imaginary
  3. two roots are real
  4. no real roots

Solution

Given, $x^2-5|x|-14=0$ $\begin{array}{ll}\Rightarrow & |x|^2-5|x|-14=0 \\ \Rightarrow & (|x|-7)(|x|+2)=0\end{array}$ $=|x|=7,|x| \neq-2$ $\therefore$ All roots are real.

Asked in: AP EAMCET 2021 (24 Aug Shift 2)

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