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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. 9.45 (page 891)

Solve by using the Quadratic Formula: $3 m^{2} + 12 m + 7 = 0$

Short Answer

Expert verified

The solution of the quadratic equation is $m = \frac{- 6 卤 \sqrt{15}}{3}$

Step by step solution

01

Given information

We are given an equation $3 m^{2} + 12 m + 7 = 0$

02

Identify the values of a,b,c

On comparing the equation with standard equation we get $a = 3, b = 12, c = 7$

03

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

The quadratic formula can be given as

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

On substituting the values in the formula we get

$m = \frac{- 12 卤 \sqrt{144 - 4 (3) (7)}}{2 (3)}$

04

Simplify

We get,

$m = \frac{- 12 卤 \sqrt{144 - 84}}{6} m = \frac{- 12 卤 \sqrt{60}}{6} m = \frac{- 12 卤 2 \sqrt{15}}{6}$

05

Factor out and remove the common factor

We take out and remove the common factor

$m = \frac{2 (- 6 卤 \sqrt{15})}{6} m = \frac{- 6 卤 \sqrt{15}}{3}$

06

Conclusion

The solution of the quadratic equation is $m = \frac{- 6 卤 \sqrt{15}}{3}$

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