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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q.124 (page 898)

In the following exercises, solve by using the Quadratic Formula: $5 b^{2} + 2 b - 4 = 0$

Short Answer

Expert verified

The solution of the quadratic equation is $b = \frac{- 1 卤 \sqrt{21}}{5}$

Step by step solution

01

Given information

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

02

Identify the values of x,y,z

On comparing with standard equation we get $x = 5, y = 2, z = - 4$

03

Give quadratic formula and substitute the values in it

The quadratic formula can be given as

$b = \frac{- y 卤 \sqrt{y^{2} - 4 x z}}{2 x}$

On substituting the values we get

$b = \frac{- 2 卤 \sqrt{4 - 4 (5) (- 4)}}{2 (5)}$

04

Simplify

On simplifying we get

$b = \frac{- 2 卤 \sqrt{4 + 80}}{10} b = \frac{- 2 卤 \sqrt{84}}{10} b = \frac{- 2 卤 2 \sqrt{21}}{10}$

05

Take out and remove the common factor

We have

$b = \frac{- 2 卤 2 \sqrt{21}}{10} b = \frac{2 (- 1 卤 \sqrt{21})}{10} b = \frac{- 1 卤 \sqrt{21}}{10}$

06

Conclusion

The solution of the quadratic equation is $b = \frac{- 1 卤 \sqrt{21}}{5}$

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