Chapter 6: Q 6.96 (page 619)

Solve $123 b = - 6 - 60 b^{2}$

Short Answer

Expert verified

The value is $- \frac{1}{20}, - 2$

Step by step solution

Given information

Given the equation $123 b = - 6 - 60 b^{2}$ $123 b = - 6 - 60 b^{2}$

Write the quadratic equation in standard form

The equation is written as follows;

$123 b = - 6 - 60 b^{2} - 60 b^{2} - 123 b - 6 = 0 60 b^{2} + 123 b + 6 = 0 3 (20 b^{2} + 41 b + 2) = 0$

Use zero factor property and calculate the value

Further solving, we get

$20 b^{2} + 41 b + 2 = 0 20 b^{2} + 40 b + b + 2 = 0 20 b (b + 2) + 1 (b + 2) = 0 (20 b + 1) (b + 2) = 0 b = - \frac{1}{20}, - 2$

Check the value

Checking, we get

$123 (- \frac{1}{20}) = - 6 - 60 {(- \frac{1}{20})}^{2} - \frac{123}{20} = - 6 - \frac{60}{400} \frac{- 123}{20} = - 6 - \frac{3}{20} \frac{- 123}{20} = \frac{- 123}{20}$

Checking for another point

Checking, we get

$123 (- 2) = - 6 - 60 {(- 2)}^{2} - 246 = - 6 - 240 - 246 = - 246$

So the value is correct

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Solve $123 b = - 6 - 60 b^{2}$

Short Answer

Step by step solution

Given information

Write the quadratic equation in standard form

Use zero factor property and calculate the value

Check the value

Checking for another point

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Solve123b=-6-60b2

Short Answer

Step by step solution

Given information

Write the quadratic equation in standard form

Use zero factor property and calculate the value

Check the value

Checking for another point

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Decision Maths

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve $123 b = - 6 - 60 b^{2}$