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Chapter 17: Problem 475

Solve the equation \(\mathrm{x}^{2}+5 \mathrm{x}+6=0\) by the quadratic formula.

Short Answer

Expert verified
The roots of the quadratic equation \(x^2 + 5x + 6 = 0\) are \(x_1 = -2\) and \(x_2 = -3\).

Step by step solution

01

Identify the coefficients of the quadratic equation

From the given equation \(x^2 + 5x + 6 = 0\), we can see that \(a = 1\), \(b = 5\), and \(c = 6\).
02

Apply the quadratic formula

We have the quadratic formula \[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\] Plug in the values \(a = 1\), \(b = 5\), and \(c = 6\) into the formula: \[x = \frac{-5 \pm \sqrt{5^2 - 4(1)(6)}}{2(1)}\]
03

Simplify the expression under the square root

Calculate the value inside the square root: \[5^2 - 4(1)(6) = 25 - 24 = 1\] The quadratic formula now becomes: \[x = \frac{-5 \pm \sqrt{1}}{2}\]
04

Calculate the roots (x values)

Now we have two possible solutions: \(x = \frac{-5 + \sqrt{1}}{2}\) and \(x = \frac{-5 - \sqrt{1}}{2}\) Calculate the values: \(x = \frac{-5 + 1}{2} = \frac{-4}{2} = -2\) \(x = \frac{-5 - 1}{2} = \frac{-6}{2} = -3\) So, we have the roots \(x_1 = -2\) and \(x_2 = -3\).

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Most popular questions from this chapter

Solve the equation \(\sqrt{(x+1)}+\sqrt{(2 x+3)-\sqrt{(} 8 x+1)}=0\).

Find the equation whose roots are \(3+\sqrt{2}\) and \(3-\sqrt{2}\).

Find the values of the constant \(\mathrm{k}\) in the equation \(2 \mathrm{x}^{2}-\mathrm{kx}+3 \mathrm{k}=0\) if the difference of the roots is \(5 / 2\)

Use the quadratic formula to solve the equation \(3 x^{2}+4 x-5=0\)

Solve \(x^{2}+2 x-5=0\)
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