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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.444. (page 983)

Solve by using the quadratic formula.
$4 b^{2} - b + 8 = 0$

Short Answer

Expert verified

The solution is $b = \frac{1 卤 \sqrt{127} i}{8}$ .

Step by step solution

01

Step 1. Given information.

The given equation is $4 b^{2} - b + 8 = 0$ .

02

Step 2. Write the equation in standard form.

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

$\begin{array}{rcl} 4 b^{2} - b + 8 & = & 0 \\ 4 b^{2} + (- 1) b + 8 & = & 0 \end{array}$

So, here $a = 4, b = - 1, c = 8$ .

03

Step 3. Apply the quadratic formula.

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

$\begin{array}{rcl} b & = & \frac{- (- 1) 卤 \sqrt{{(- 1)}^{2} - 4 脳 4 脳 8}}{2 脳 4} 鈰� 鈰� 鈰� (a = 4, b = - 1, c = 8) \\ = & \frac{1 卤 \sqrt{1 - 128}}{8} \\ = & \frac{1 卤 \sqrt{- 127}}{8} \\ = & \frac{1 卤 \sqrt{127} \sqrt{- 1}}{8} \\ = & \frac{1 卤 \sqrt{127} i}{8} 鈰� 鈰� 鈰� 鈰� 鈰� (i = \sqrt{- 1}) \end{array}$

04

Step 4. Simplified answer.

Hence, the required solution is $b = \frac{1 卤 \sqrt{127} i}{8}$ .

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Most popular questions from this chapter

Solve :- $x - 6 \sqrt{x} + 8 = 0$

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