Question

The quadratic equations $x^2+15\left|x\right|+14=0$ has

• A. only positive solutions
• B. only negative solutions
• C. no solution
• D. both positive and negative solutions

Answer 1

The correct option is C

no solution

Explanation for correct option:

Evaluate the given quadratic equation

Given, $x^2+15\left|x\right|+14=0$

$$\begin{gathered} x^2+15\left|x\right|+14=0 \\ \Rightarrow {\left|x\right|}^2+15\left|x\right|+14=0 \\ \Rightarrow {\left|x\right|}^2+14\left|x\right|+\left|x\right|+14=0 \\ \Rightarrow \left|x\right|\left(\left|x+14\right|\right)+1\left(\left|x\right|+14\right)=0 \\ \Rightarrow \left(\left|x\right|+1\right)\left(\left|x\right|+14\right)=0 \\ \Rightarrow \left|x\right|=-1⋮\left|x\right|=-14 \end{gathered}$$

Hence, $\left|x\right|$is not negative, so $x^2+15\left|x\right|+14=0$ has no solution, option (C) is correct.