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

Given information.

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

Use the quadratic formula.

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

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.

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

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

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

Short Answer

Step by step solution

Given information.

Use the quadratic formula.

Solve both the equations for r.

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In the following exercises, solve by using the Quadratic Formula.r2-r-42=0

Short Answer

Step by step solution

Given information.

Use the quadratic formula.

Solve both the equations for r.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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