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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.116 (page 898)

In the following exercises, solve by using the Quadratic Formula. $3 q^{2} + 8 q - 3 = 0$

Short Answer

Expert verified

The solution of the quadratic equation is $q = - 3$ and $q = \frac{1}{3}$

Step by step solution

01

Given information

We are given a quadratic equation $3 q^{2} + 8 q - 3 = 0$

02

Identify the values of a,b,c

On comparing with standard equation we get $a = 3, b = 8, c = - 3$

03

We write the quadratic formula and substitute the values in it

The quadratic formula can be given as

$q = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$

On substituting the values we get

$q = \frac{- 8 卤 \sqrt{64 - 4 (3) (- 3)}}{2 (3)}$

04

Simplify

On simplifying we get

$q = \frac{- 8 卤 \sqrt{64 + 36}}{6} q = \frac{- 8 卤 \sqrt{100}}{6} q = \frac{- 8 卤 10}{6}$

On further simplifying we get

$q = \frac{- 8 + 10}{6} q = \frac{2}{6} q = \frac{1}{3}$ and $q = \frac{- 8 - 10}{6} q = \frac{- 18}{6} q = - 3$

05

Conclusion

The solution of the above equation is $q = - 3$ and $q = \frac{1}{3}$

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