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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.122 (page 898)

In the following exercises, solve by using the Quadratic Formula: $2 p^{2} + 8 p + 5 = 0$

Short Answer

Expert verified

The solution of the quadratic equation is $p = \frac{- 4 卤 \sqrt{6}}{2}$

Step by step solution

01

Given information

We are given a quadratic equation $2 p^{2} + 8 p + 5 = 0$

02

Identify the values of a,b,c

On comparing with standard equation we get $a = 2, b = 8, c = 5$

03

Write quadratic formula and substitute the values in it

The quadratic formula can be given as

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

On substituting the values we get

$p = \frac{- 8 卤 \sqrt{64 - 4 (2) (5)}}{2 (2)}$

04

Simplify

On simplifying we get

$p = \frac{- 8 卤 \sqrt{64 - 40}}{4} p = \frac{- 8 卤 \sqrt{24}}{4} p = \frac{- 8 卤 2 \sqrt{6}}{4}$

05

Taking out and removing the common factor

We have,

$p = \frac{- 8 卤 2 \sqrt{6}}{4} p = \frac{2 (- 4 卤 \sqrt{6})}{4} p = \frac{- 4 卤 \sqrt{6}}{2}$

06

Conclusion

The solution of the quadratic equation is $p = \frac{- 4 卤 \sqrt{6}}{2}$

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Most popular questions from this chapter

Solve quadratic equation $x^{2} - 6 x + 9 = 12$ using square root property

Use the Discriminant to Predict the Number of Solutions of a Quadratic Equation.

In the following exercises, determine the number of solutions for each quadratic equation.

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In the following exercises, solve by using the Quadratic Formula: $t^{2} + 13 t = - 40$

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