Chapter 9, Problem 9PFA

To determine

To select correct solution of the quadratic equation from the given options.

Answer to Problem 9PFA

Option D. -1.1 or 1.5

Explanation of Solution

Given information :

The function provided is $5x^2-2x=8$ .

Option A. no solutions

Option B. 1.1 or -1.5

Option C. 1.1

Option D. -1.1 or 1.5

Formula used :

To calculate the time when height of ball is 0 feet, use the formula to find roots of a quadratic equation. This can be found by using $t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . Here ‘a’, ‘b’ and ‘c’ are the co-efficient of the given equation.

Here, $a=5,b=-2\text{ and}c=-8$ .

Calculation :

  $x=\frac{-(-2)\pm \sqrt{{(-2)}^2-4\times (5)\times (-8)}}{2(5)}$

Putting the values in the formula.

  $x=\frac{2\pm \sqrt{164}}{-10}$

Removing square root.

  $x=\frac{2\pm 12.8}{10}$

One of the roots is

  $x=-1.08$

This is the first root.

Second root is.

  $x=\frac{14.8}{10}$

Dividing the fraction.

  $x=1.48$

Rounding off to the nearest tenth; $x=-1.1,1.5$