Chapter 4.8, Problem 5BGP

To determine

To Find: Algebraic solution of the given inequality

Answer to Problem 5BGP

  $x=-5\text{ or }x=-6$

Explanation of Solution

Given:

  $x^2+11x+30\ge 0$

Formula Used:

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

  $\text{or }\left(\text{Factorisation Method}\right)$

Calculation:

  $\begin{array}{l}{x}^2+11x+30\ge 0\\ \Rightarrow x^2+11x+30=0\left(1\right)\\ \Rightarrow x^2+5x+6x+30=0\left(\text{using middle term split property of quadratic equation}\right)\left(2\right)\\ \Rightarrow -x\left(x+5\right)+6\left(x+5\right)=0\left(3\right)\\ \Rightarrow \left(x+5\right)\left(x+6\right)=0\left(4\right)\\ \Rightarrow x+5=0\text{ or x+6}=0\left(\text{using zero product property}\right)\\ \Rightarrow x=-5\text{ or }x=-6\end{array}$