Chapter 12.3, Problem 3WE

To determine

To solve: the equation $5z^2-11z+2=0$ using quadratic formula. Give irrational roots in simplest radical form and then approximate them to the nearest tenth.

Answer to Problem 3WE

The required answer is: solution set is 2, 0.2

Explanation of Solution

Given information:

The given equation: $5z^2-11z+2=0$

Calculation:

  $\begin{array}{l}5z^2-11z+2=0\\ z=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\end{array}$

(Quadratic formula)

Where $a=5,b=-11andc=2$

  $z=\frac{-(-11)\pm \sqrt{{(-11)}^2-4(5)(2)}}{2(5)}$

(Remove the brackets)

  $\begin{array}{l}=\frac{11\pm \sqrt{121-40}}{10}\\ =\frac{11\pm \sqrt{81}}{10}\\ =\frac{11\pm 9}{10}\end{array}$

(Simplify)

Here, $z=\frac{11+9}{10}=\frac{20}{10}=2$

Or   $z=\frac{11-9}{10}=\frac{2}{10}=0.2$

Therefore the solution set is 2, 0.2