Chapter 9, Problem 20PT

To determine

To solve the given equation using quadratic formula.

Answer to Problem 20PT

The values of x are -3 and 2.5.

Explanation of Solution

Given information :

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

Formula used :

The quadratic formula to find the roots of a quadratic equation is $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ .

Where, a and b are the coefficients of $x^2$ , $x$ and c is the constant. Here $a=2$ , $b=1$ and $c=-15$

Calculation :

  $x=\frac{-1\pm \sqrt{1^2-4\times 2\times -15}}{2\times 2}$

Putting the values a, b and c in the formula.

  $x=\frac{-1\pm \sqrt{1^2-4\times 2\times -15}}{2\times 2}$

Simplifying this

  $=\frac{-1\pm \sqrt{1+120}}{4}$

Calculating the numbers under the square root.

  $=\frac{-1\pm \sqrt{121}}{4}$

Removing the square root.

  $=\frac{-1\pm 11}{4}$

Simplifying this to get roots.

  $x=\frac{-1-11}{4}$

Solving for one root.

  $=\frac{-12}{4}$

Dividing the fraction

  $=-3$

This is one root.

  $x=\frac{-1+11}{4}$

Solving for one root.

  $=\frac{10}{4}$

Dividing the fraction

  $=2.5$

This is the other root.