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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.443. (page 983)

Solve by using the quadratic formula.
$6 a^{2} - 5 a + 2 = 0$

Short Answer

Expert verified

The solution is $a = \frac{5 卤 \sqrt{23} i}{12}$ .

Step by step solution

01

Step 1. Given information.

The given equation is $6 a^{2} - 5 a + 2 = 0$ .

02

Step 2. Write the equation in standard form.

The standard form of the quadratic equation is $a x^{2} + b x + c = 0$ .

$\begin{array}{rcl} 6 a^{2} - 5 a + 2 & = & 0 \\ 6 a^{2} + (- 5) a + 2 & = & 0 \end{array}$

So, here $a = 6, b = - 5, c = 2$ .

03

Step 3. Apply the quadratic formula.

The quadratic formula is $a = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$ .

$\begin{array}{rcl} a & = & \frac{- (- 5) 卤 \sqrt{{(- 5)}^{2} - 4 脳 6 脳 2}}{2 脳 6} 鈰� 鈰� 鈰� 鈰� 鈰� (a = 6, b = - 5, c = 2) \\ = & \frac{5 卤 \sqrt{25 - 48}}{12} \\ = & \frac{5 卤 \sqrt{- 23}}{12} \\ = & \frac{5 卤 \sqrt{23} 路 \sqrt{- 1}}{12} \\ = & \frac{5 卤 \sqrt{23} 路 i}{12} 鈰� 鈰� 鈰� 鈰� 鈰� 鈰� 鈰� (i = \sqrt{- 1}) \end{array}$

04

Step 4. Simplified answer.

Hence, the required solution is $a = \frac{5 卤 \sqrt{23} 路 i}{12}$ .

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