Chapter 4, Problem 21AR

To determine

To solve the given equation, $x^2+5x+2=0$ by factoring or quadratic formula.

Answer to Problem 21AR

  $x=\frac{-5+\sqrt{17}}{2},\frac{-5-\sqrt{17}}{2}$

Explanation of Solution

Given:

The equation is, $x^2+5x+2=0$

Calculation:

We can solve the given equation by using quadratic formula.

That is,

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Which is in the form of $a{x}^2+bx+c=0$ . Where, $a=1,b=5\text{ and c = 2}$ .

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

  $\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-5\pm \sqrt{5^2-4\left(1\right)\left(2\right)}}{2\left(1\right)}\\ x=\frac{-5\pm \sqrt{25-8}}{2}\\ x=\frac{-5+\sqrt{17}}{2},\frac{-5-\sqrt{17}}{2}\end{array}$

Therefore, the roots for the given equation, $x^2+5x+2=0$ are $x=\frac{-5+\sqrt{17}}{2},\frac{-5-\sqrt{17}}{2}$ .