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Chapter 0: Problem 78

Solve each quadratic equation using the quadratic formula. $$x^{2}+5 x+2=0$$

Short Answer

Expert verified
The roots of the equation \(x^{2}+5x+2=0\) are \(\frac{-5 + \sqrt{17}}{2}\) and \(\frac{-5 - \sqrt{17}}{2}\).

Step by step solution

01

Identify coefficients

For the given quadratic equation \(x^{2}+5x+2=0\), the coefficients are \(a=1\), \(b=5\), and \(c=2\).
02

Substitute into the quadratic formula

Next, substitute the coefficients \(a\), \(b\), and \(c\) into the quadratic formula, \(x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\). This gives \(x = \frac{-5 \pm \sqrt{5^2-4(1)(2)}}{2*1} = \frac{-5 \pm \sqrt{25-8}}{2}\).
03

Simplify the expression

Simplify the expression inside the square root and the fraction to obtain the roots. This gives \(x = \frac{-5 \pm \sqrt{17}}{2}\). Therefore, the roots of the quadratic equation \(x^{2}+5x+2=0\) are \(\frac{-5 + \sqrt{17}}{2}\) and \(\frac{-5 - \sqrt{17}}{2}\).

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Most popular questions from this chapter

Perform the indicated operations. Simplify the result, if possible. $$\left(\frac{1}{a^{3}-b^{3}} \cdot \frac{a c+a d-b c-b d}{1}\right)-\frac{c-d}{a^{2}+a b+b^{2}}$$

Rationalize the numerator. $$\frac{\sqrt{x}+\sqrt{y}}{x^{2}-y^{2}}$$

This will help you prepare for the material covered in the next section. Evaluate $$\frac{-b-\sqrt{b^{2}-4 a c}}{2 a}$$ for \(a=2, b=9,\) and \(c=-5\)

Explain how to divide rational expressions.

This will help you prepare for the material covered in the next section. If 6 is substituted for \(x\) in the equation $$2(x-3)-17=13-3(x+2)$$ is the resulting statement true or false?
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