Chapter 9: Q. 9.46 (page 891)

Solve by using the Quadratic Formula: $5 n^{2} + 4 n - 4 = 0$

Short Answer

Expert verified

The solution of the quadratic equation is $n = \frac{- 2 \pm 2 \sqrt{6}}{5}$

Step by step solution

Given information

We are given a quadratic equation $5 n^{2} + 4 n - 4 = 0$

Identify the values of a,b,c

On comparing with standard equation we get $a = 5, b = 4, c = - 4$

Write quadratic formula and substitute the values of a,b,c

The quadratic formula can be given as

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

On substituting the values we get

$n = \frac{- 4 \pm \sqrt{16 - 4 (5) (- 4)}}{2 (5)}$

Simplify

On simplifying we get

$n = \frac{- 4 \pm \sqrt{16 + 80}}{10} n = \frac{- 4 \pm 4 \sqrt{6}}{10}$

Factor out and remove the common factor

We get

$n = \frac{2 (- 2 \pm 2 \sqrt{6})}{10} n = \frac{- 2 \pm 2 \sqrt{6}}{5}$

Conclusion

The root of the equation is $n = \frac{- 2 \pm 2 \sqrt{6}}{5}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve by using the Quadratic Formula: $5 n^{2} + 4 n - 4 = 0$

Short Answer

Step by step solution

Given information

Identify the values of a,b,c

Write quadratic formula and substitute the values of a,b,c

Simplify

Factor out and remove the common factor

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Mechanics Maths

Statistics

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve by using the Quadratic Formula:5n2+4n-4=0

Short Answer

Step by step solution

Given information

Identify the values of a,b,c

Write quadratic formula and substitute the values of a,b,c

Simplify

Factor out and remove the common factor

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Mechanics Maths

Statistics

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve by using the Quadratic Formula: $5 n^{2} + 4 n - 4 = 0$