Chapter 7: Q. 7.150 (page 885)

Solve:
$45 b^{2} - 2 b = - 17 b$

Short Answer

Expert verified

The solutions of the quadratic equations $45 b^{2} - 2 b = - 17 b$ are $b = - \frac{1}{3}, 0$

Step by step solution

Step 1. Given Information

An equation:

$45 b^{2} - 2 b = - 17 b$

Step 2. Write the quadratic equation in standard form.

$45 b^{2} - 2 b = - 17 b 45 b^{2} - 2 b + 17 b = 0 45 b^{2} + 15 b = 0$

Step 3. Factor the quadratic expression

Factorize the equation,

$45 b^{2} + 15 b = 0 15 b (3 b + 1) = 0$

Step 4. Use the Zero-Product property

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

$15 b = 0 b = 0 3 b + 1 = 0 3 b = - 1 b = - \frac{1}{3}$

The value of b is $b = - \frac{1}{3}, 0$

Step 5. Check the answer

Check by substituting the values in the original equation,

When $b = - \frac{1}{3}$ ,

$45 {(- \frac{1}{3})}^{2} - 2 (- \frac{1}{3}) = - 17 (- \frac{1}{3}) \frac{15}{3} + \frac{2}{3} = \frac{17}{3} \frac{17}{3} = \frac{17}{3}$

When $b = 0$ ,

$45 {(0)}^{2} - 2 (0) = - 17 (0) 0 = 0$

Hence the equations hold true.

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Solve:
$45 b^{2} - 2 b = - 17 b$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Write the quadratic equation in 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:45b2-2b=-17b

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Write the quadratic equation in 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

Discrete Mathematics

Calculus

Pure Maths

Applied Mathematics

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

Solve:
$45 b^{2} - 2 b = - 17 b$