Chapter 6, Problem 14CR

To determine

To Solve:

  $3x^2+14=8$

Answer to Problem 14CR

(c)

Explanation of Solution

Given :

The equation is :

  $3x^2+14=8$

  $\begin{array}{l}a.\left\{\pm 2i\right\}\\ b.\left\{\pm \sqrt{2}\right\}\\ c.\left\{\pm i\sqrt{2}\right\}\\ d.\left\{\pm 2\right\}\end{array}$

Calculation:

Given:

  $\begin{array}{l}3x^2+14=8\\ \Rightarrow 3x^2=8-\mathrm{14..........}[\text{subtract 14 from each side]}\\ \Rightarrow 3x^2=-6\\ \Rightarrow \frac{3x^2}{3}=\frac{-6}{3}\mathrm{.............}[\text{divide each side by 3]}\\ \Rightarrow x^2=-2\\ \Rightarrow \sqrt{x^2}=\pm \sqrt{-2}\mathrm{.......}[\text{take square root each side]}\\ \Rightarrow x=\pm i\sqrt{2}\end{array}$

So, (c) is the correct option.