Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 8 - Section 8.2 - The Quadratic Formula - 8.2 Exercises: 50


$b=\{ -14,14 \}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To find the value of $ b $ such that the given equation, $ r^2-br+49=0 ,$ will have $1$ rational solution, equate the discriminant to $0$ and solve for the variable. $\bf{\text{Solution Details:}}$ In the equation above, $a= 1 ,$ $b= -b ,$ and $c= 49 .$ Using the Discriminant Formula which is given by $b^2-4ac,$ the discriminant is \begin{array}{l}\require{cancel} (-b)^2-4(1)(49) \\\\= b^2-196 .\end{array} Equating the discriminant to $0$ so that the given equation will have $1$ rational solution, then \begin{array}{l}\require{cancel} b^2-196=0 \\\\ b^2=196 .\end{array} Taking the square root of both sides, then \begin{array}{l}\require{cancel} b=\pm\sqrt{196} \\\\ b=\pm14 .\end{array} Hence, the given equation has $1$ rational solution when $ b=\{ -14,14 \} .$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.