Chapter 9.5, Problem 33P

Solve each equation. If necessary, round to the nearest hundredth. If there is no solution, write no solution.

$2a^2-3a+4=0$

To determine

To solve : the equation

Answer to Problem 33P

The solution of the equation has no solution

Explanation of Solution

Given information :

The equation is

  $2a^2-3a+4=0$

Formula used :

Sridhar Acharya  $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Calculation :

The solution of the equation is

  $\begin{array}{l}2a^2-3a+4=0\\ a=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ a=\frac{-\left(-3\right)\pm \sqrt{{\left(-3\right)}^2-4\cdot 2\cdot 4}}{2\cdot 2}\text{ Where }b=-3,a=2,c=4\\ a=\frac{3\pm \sqrt{9-32}}{4}\\ a=\frac{-3\pm \sqrt{-23}}{4}\end{array}$

Therefore, the equation has no solution because there is negative sing under the square root.

Hence, the solution of the equation has no solution.