Chapter 9: Q.189 (page 906)

In the following exercises, solve equations in Quadratic Form for $6 x^{- 2} + 13 x^{- 1} + 5 = 0$ .

Short Answer

Expert verified

The solution of the equation is $x = - \frac{3}{5}, x = - 2$ .

Step by step solution

Step 1. Given Information.

The given equation is $6 x^{- 2} + 13 x^{- 1} + 5 = 0$ .

Step 2. Simplify

Simplifying $6 x^{- 2} + 13 x^{- 1} + 5 = 0$

$\frac{6}{x^{2}} + \frac{13}{x} + 5 = 0 6 + 13 x + 5 x^{2} = 0$

Step 3. Solve Quadratic equation.

Using quadratic formula:-

$5 x^{2} + 13 x + 6 = 0$

$x_{1, 2} = \frac{- 13 \pm \sqrt{13^{2} - 4 \cdot 5 \cdot 6}}{2 \cdot 5} x_{1, 2} = \frac{- 13 \pm 7}{2 \cdot 5} x_{1} = \frac{- 13 + 7}{2 \cdot 5}, x_{2} = \frac{- 13 - 7}{2 \cdot 5} x = - \frac{3}{5}, x = - 2$

Therefore, The solution of the equation are $x = - \frac{3}{5}, x = - 2$ .

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In the following exercises, solve equations in Quadratic Form for $6 x^{- 2} + 13 x^{- 1} + 5 = 0$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Simplify

Step 3. Solve Quadratic equation.

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In the following exercises, solve equations in Quadratic Form for 6x-2 + 13x-1 + 5 = 0.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Simplify

Step 3. Solve Quadratic equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Geometry

Pure Maths

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, solve equations in Quadratic Form for $6 x^{- 2} + 13 x^{- 1} + 5 = 0$ .