Chapter 4.8, Problem 42PPS

To determine

To Find: The solution of the inequality algebraically

Answer to Problem 42PPS

  $\frac{-5-\sqrt{113}}{4}or\frac{-5+\sqrt{113}}{4}$

Explanation of Solution

Given:

  $-11\ge -2x^2-5x$

Formula Used:

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Using factorization method.

Calculation:

  $\begin{array}{l}-11\ge -2x^2-5x\\ \Rightarrow 2x^2+5x-11\le 0\\ a=2;\\ b=5;\\ c=-11\\ x=\frac{-5\pm \sqrt{{\left(5\right)}^2-4\left(2\right)\left(-11\right)}}{2\left(2\right)}\\ \Rightarrow x=\frac{-5\pm \sqrt{25+88}}{4}\\ \Rightarrow x=\frac{-5\pm \sqrt{113}}{4}\\ \Rightarrow x=\frac{-5-\sqrt{113}}{4}or\frac{-5+\sqrt{113}}{4}\end{array}$