Chapter 9: Q. 138 (page 898)

In the following exercises, solve by using the Quadratic Formula.
$\frac{1}{3} n^{2} + n = - \frac{1}{2}$

Short Answer

Expert verified

The solutions of the given equation are $n = - \frac{3}{2} \pm \frac{\sqrt{3}}{2}$ .

Step by step solution

Step 1. Write the quadratic equation in standard form.

The given equation is:

$\frac{1}{3} n^{2} + n = - \frac{1}{2}$

The given equation can be written as:

$\begin{array}{rcl} \frac{1}{3} n^{2} + n + \frac{1}{2} & = & 0 \\ \frac{2 n^{2} + 6 n + 3}{6} & = & 0 \\ 2 n^{2} + 6 n + 3 & = & 0 \end{array}$

Step 2. Substitute the values in Quadratic Formula.

Quadratic Formula for the equation $a x^{2} + b x + c = 0$ is:

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

In the given equation, $a = 2, b = 6, c = 3$ . Substitute these values in Quadratic Formula.

$n = \frac{- 6 \pm \sqrt{(6)^{2} - 4 (2) (3)}}{2 (2)}$

Step 3. Simplify the value.

On simplification, we get

$\begin{array}{rcl} n & = & \frac{- 6 \pm \sqrt{36 - 24}}{4} \\ n & = & \frac{- 6 \pm \sqrt{12}}{4} \\ n & = & \frac{- 6}{4} \pm \frac{2 \sqrt{3}}{4} \\ n & = & - \frac{3}{2} \pm \frac{\sqrt{3}}{2} \end{array}$

Step 4. Conclusion.

The solutions of the given equation are $n = - \frac{3}{2} \pm \frac{\sqrt{3}}{2}$ .

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In the following exercises, solve by using the Quadratic Formula.
$\frac{1}{3} n^{2} + n = - \frac{1}{2}$

Short Answer

Step by step solution

Step 1. Write the quadratic equation in standard form.

Step 2. Substitute the values in Quadratic Formula.

Step 3. Simplify the value.

Step 4. Conclusion.

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In the following exercises, solve by using the Quadratic Formula.13n2+n=-12

Short Answer

Step by step solution

Step 1. Write the quadratic equation in standard form.

Step 2. Substitute the values in Quadratic Formula.

Step 3. Simplify the value.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Pure Maths

Theoretical and Mathematical Physics

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, solve by using the Quadratic Formula.
$\frac{1}{3} n^{2} + n = - \frac{1}{2}$