Chapter 8.2, Problem 82SR

To determine

To solve: the equation and state the type of root.

Answer to Problem 82SR

The value of equation is $x=\frac{5\pm \sqrt{71}i}{24}$ and the roots are imaginary.

Explanation of Solution

Given information:

The equation is $2x^2-5x+12=0$ .

Calculation: to solve the equation, first use the quadratic and simplify,

  $\begin{array}{l}2x^2-5x+12=0\\ x=\frac{-\left(-5\right)\pm \sqrt{{\left(-5\right)}^2-4\left(2\right)\left(12\right)}}{2\left(12\right)}\text{ [use the quadratic formula and substitute]}\\ x=\frac{5\pm \sqrt{25-96}}{24}\text{ [multiply]}\\ x=\frac{5\pm \sqrt{71}i}{24}\text{ [simplify]}\end{array}$

Thus, the roots of the equation is $x=\frac{5\pm \sqrt{71}i}{24}$ and the roots are imaginary.