Chapter 9, Problem 47SGR

To determine

To compute the value of the equation using quadratic formula.

Answer to Problem 47SGR

The value of x is -0.71 and 0.47.

Explanation of Solution

Given information :

The function provided is $21x^2+5x-7=0$ .

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, $a=21,b=5\text{ and}c=-7$ .

Calculation :

  $x=\frac{-(5)\pm \sqrt{{(5)}^2-4\times (21)\times (-7)}}{2(21)}$

Putting the values in the formula.

  $x=\frac{-5\pm \sqrt{25+588}}{42}$

Simplifying

  $x=\frac{-5\pm \sqrt{613}}{42}$

Removing square root.

  $x=\frac{-5\pm 24.8}{42}$

One of the roots is

  $x=\frac{-5-24.8}{42}$

Simplifying

  $x=-0.71$

This is the first root.

Second root is.

  $x=\frac{-5+24.8}{42}$

Simplifying

  $x=0.47$