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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.123 (page 898)

In the following exercises, solve by using the Quadratic Formula: $2 a^{2} - 6 a + 3 = 0$

Short Answer

Expert verified

The solution of the quadratic equation is $a = \frac{3 卤 \sqrt{3}}{2}$

Step by step solution

01

Given information

We are given a quadratic equation $2 a^{2} - 6 a + 3 = 0$

02

Identify the values of x,y,z

On comparing with standard equation we get $x = 2, y = - 6, z = 3$

03

Write the quadratic formula and substitute the values in it

The quadratic formula can be given as

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

On substituting the values we get

$a = \frac{6 卤 \sqrt{36 - 4 (2) (3)}}{2 (2)}$

04

Simplify

On simplifying we get,

$a = \frac{6 卤 \sqrt{36 - 24}}{4} a = \frac{6 卤 \sqrt{12}}{4} a = \frac{6 卤 2 \sqrt{3}}{4}$

05

Take out and remove the common factor

We get

$a = \frac{2 (3 卤 \sqrt{3})}{4} a = \frac{3 卤 \sqrt{3}}{2}$

06

Conclusion

The solution of the quadratic equation of $a = \frac{3 卤 \sqrt{3}}{2}$

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