Chapter 1.8, Problem 12E

Solution

Find the complex solutions of the equation $2x^2-16x+50=0$ for $\left(s\right)$ .

The complex solution for the quadratic equation is $x=\left\{4+3i,4-3i\right\}$ , so option $\left(A\right)$ is correct.

Given:

The quadratic equation is $2x^2-16x+50=0$ .

Concept used:

Any quadratic equation of the form $a{x}^2+bx+c=0\text{ where }a\ne 0$ has the roots $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\mathrm{......}\left(1\right)$

Calculation:

The solution $\left(x\right)$ for the quadratic equation $2x^2-16x+50=0$ can be evaluated with the help of formula $\left(1\right)$ . Therefore,

  $\begin{array}{c}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\mathrm{......}\left(\text{From }\left(1\right)\right)\\ =\frac{-\left(-16\right)\pm \sqrt{{\left(-16\right)}^2-4\left(2\right)\left(50\right)}}{2\left(2\right)}\mathrm{......}\left(\because 2x^2-16x+50=0\right)\\ =\frac{16\pm \sqrt{256-400}}{4}\\ =\frac{16\pm i\sqrt{144}}{4}\\ =\frac{16\pm i12}{4}\\ \frac{16+12i}{4},\frac{16-12i}{4}\\ =\left\{4+3i,4-3i\right\}\end{array}$

Since the complex solution for the quadratic equation is $x=\left\{4+3i,4-3i\right\}$ , so option $\left(A\right)$ is correct.