Chapter 4.2, Problem 32E

To determine

To solve: The equation $p^2+2p+8=0$

Answer to Problem 32E

  $x=\frac{-2+2i\sqrt{7}}{2}\text{ or }x=\frac{-2-2i\sqrt{7}}{2}$

Explanation of Solution

Given information: $p^2+2p+8=0$

Calculation:

Given

  $p^2+2p+8=0$

Discriminant

  $b^2-4ac={\left(2\right)}^2-4\ast 1\left(8\right)=4-32=-28$

Quadratic formula

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substitute values

  $x=\frac{-2\pm \sqrt{-28}}{2}$

  $\begin{array}{l}x=\frac{-2\pm i\sqrt{28}}{2}\\ x=\frac{-2\pm 2i\sqrt{7}}{2}\end{array}$

  $x=\frac{-2+2i\sqrt{7}}{2}\text{ or }x=\frac{-2-2i\sqrt{7}}{2}$