Chapter 7: Q. 7.155 (page 887)

Solve:
$8 x^{3} = 24 x^{2} - 18 x$

Short Answer

Expert verified

The solutions of the quadratic equations $8 x^{3} = 24 x^{2} - 18 x$ are $x = 0, \frac{3}{2}$

Step by step solution

Step 1. Given Information.

An equation:

$8 x^{3} = 24 x^{2} - 18 x$

Step 2. Write the quadratic equation in the standard form.

$8 x^{3} = 24 x^{2} - 18 x 8 x^{3} - 24 x^{2} + 18 x = 0 2 x (4 x^{2} - 12 x + 9) = 0$

Step 3. Factor the quadratic expression.

$2 x (4 x^{2} - 12 x + 9) = 0 2 x (4 x^{2} - 6 x - 6 x + 9) = 0 2 x {(2 x - 3)}^{2} = 0$

Step 4. Use the Zero-Product property.

Use the Zero Product Property and set each factor to zero.

$2 x = 0 x = 0 2 x - 3 = 0 x = \frac{3}{2}$

The value ofx is $x = 0, \frac{3}{2}$

Step 5. Check the answer.

Check by substituting the values in the original equation,

When $x = 0$ ,

$8 (0) = 24 (0) - 18 (0) 0 = 0$

When $x = \frac{3}{2}$ ,

$8 {(\frac{3}{2})}^{3} = 24 {(\frac{3}{2})}^{2} - 18 (\frac{3}{2}) 27 = 54 - 27$

Hence the equations hold true.

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Solve:
$8 x^{3} = 24 x^{2} - 18 x$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Write the quadratic equation in the standard form.

Step 3. Factor the quadratic expression.

Step 4. Use the Zero-Product property.

Step 5. Check the answer.

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Solve:8x3=24x2-18x

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Write the quadratic equation in the standard form.

Step 3. Factor the quadratic expression.

Step 4. Use the Zero-Product property.

Step 5. Check the answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Logic and Functions

Theoretical and Mathematical Physics

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

Solve:
$8 x^{3} = 24 x^{2} - 18 x$