Chapter 4, Problem 24AR

To determine

To solve the given equation, $x^2+3x-2=0$ by factoring or quadratic formula.

Answer to Problem 24AR

  $x=\frac{-3+\sqrt{17}}{2},\frac{-3-\sqrt{17}}{2}$

Explanation of Solution

Given:

The equation is, $x^2+3x-2=0$

Calculation:

We can solve the given equation by using quadratic formula.

That is,

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

The given equation $x^2+3x-2=0$ , which is in the form of $a{x}^2+bx+c=0$ . Where, $a=1,b=3\text{ and c =-2}$

Now, Substitute the values in the formula then we get that,

  $\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-\left(3\right)\pm \sqrt{{\left(3\right)}^2-4\left(1\right)\left(-2\right)}}{2\left(1\right)}\\ x=\frac{-\left(3\right)\pm \sqrt{9+8}}{2}\\ x=\frac{-\left(3\right)\pm \sqrt{17}}{2}\\ x=\frac{-3\pm \sqrt{17}}{2}\\ x=\frac{-3+\sqrt{17}}{2},\frac{-3-\sqrt{17}}{2}\end{array}$

Therefore, the roots for the given equation, $x^2+3x-2=0$ are $x=\frac{-3+\sqrt{17}}{2},\frac{-3-\sqrt{17}}{2}$ .