Chapter 9, Problem 49SGR

To determine

To compute the value of the equation using quadratic formula.

Answer to Problem 49SGR

The value of f is -5 and 1.5.

Explanation of Solution

Given information :

The function provided is $2f^2+7f-15=0$ .

Formula used :

Quadratic formula is $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . Here ‘a’, ‘b’ and ‘c’ are the co-efficient of the given equation.

Here, $a=2,b=7\text{ and}c=-15$ .

Calculation :

  $f=\frac{-(7)\pm \sqrt{{(7)}^2-4\times (2)\times (-15)}}{2(2)}$

Putting the values in the formula.

  $f=\frac{-7\pm \sqrt{49+120}}{4}$

Simplifying

  $f=\frac{-7\pm \sqrt{169}}{4}$

Removing square root.

  $f=\frac{-7\pm 13}{4}$

One of the roots is

  $f=\frac{-7-13}{4}$

Simplifying

  $f=-5$

This is the first root.

Second root is.

  $f=\frac{-7+13}{4}$

Simplifying

  $f=1.5$