Chapter 9.5, Problem 31P

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

$p^2+3p+2=-1$

To determine

To solve : the equation

Answer to Problem 31P

The solution of the equation has no solution

Explanation of Solution

Given information :

The equation is

  $p^2+3p+2=-1$

Formula used :

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

Calculation :

The solution of the equation is

  $\begin{array}{l}{p}^2+3p+2=-1\\ p^2+3p+2+1=0\\ p^2+3p+3=0\\ p=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ b=\frac{-3\pm \sqrt{{\left(3\right)}^2-4\cdot 1\cdot 3}}{2\cdot 1}\text{ Where }b=3,a=1,c=3\\ b=\frac{-3\pm \sqrt{9-12}}{2}\\ p=\frac{-3\pm \sqrt{-3}}{2}\end{array}$

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

Hence, the solution of the equation has no solution.