Chapter 12.3, Problem 1WE

To determine

To solve: the equation $x^2-3x-10=0$ using quadratic formula. Give irrational roots in simplest radical form and then approximate them to the nearest tenth.

Answer to Problem 1WE

The required answer is: solution set is 5,-2

Explanation of Solution

Given information:

The given equation: $x^2-3x-10=0$

Calculation:

  $\begin{array}{l}{x}^2-3x-10=0\\ x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\end{array}$

(Quadratic formula)

Where $a=1,b=-3andc=-10$

  $x=\frac{-(-3)\pm \sqrt{{(-3)}^2-4(1)(-10)}}{2(1)}$

(Remove the brackets)

  $\begin{array}{l}=\frac{3\pm \sqrt{9+40}}{2}\\ =\frac{3\pm \sqrt{49}}{2}\\ =\frac{3\pm 7}{2}\end{array}$

(Simplify)

Here, $x=\frac{3+7}{2}=\frac{10}{2}=5$

Or   $x=\frac{3-7}{2}=\frac{-4}{2}=-2$

Therefore the solution set is 5,-2