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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 10: Q 269. (page 1236)

In the following exercises, solve by using the Quadratic Formula.
$r^{2} - r - 42 = 0$

Short Answer

Expert verified

The solutions are $r = - 6 a n d r = 7 .$

Step by step solution

01

Given information.

The given information is $r^{2} - r - 42 = 0$

02

Use the quadratic formula.

The quadratic formula for the equation $a x^{2} + b x + c = 0$ is $x = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a} .$

Now we compare the given equation with the standard form we get $a = 1, b = - 1 a n d c = - 42 .$

Now we substitute these values in the quadratic formula.

$r = \frac{- (- 1) 卤 \sqrt{{(- 1)}^{2} - 4 (1) (- 42)}}{2 (1)} r = \frac{1 卤 \sqrt{1 + 168}}{2} r = \frac{1 卤 \sqrt{169}}{2} r = \frac{1 卤 13}{2}$

The two equations arelocalid="1653588225244" $r = \frac{1 + 13}{2} a n d r = \frac{1 - 13}{2} .$

03

Solve both the equations for r.

$r = \frac{1 + 13}{2} r = \frac{14}{2} r = 7 O r r = \frac{1 - 13}{2} r = \frac{- 12}{2} r = - 6$

Therefore, the two solutions are $r = - 6 a n d r = 7 .$

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