EBK PRECALCULUS W/LIMITS
EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Concept explainers

Limits
When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…
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Question
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Chapter 2.7, Problem 90E

(a)

To determine

To find: the interval (s) for b such that equation has at least one real solution.

(a)

Expert Solution
Check Mark

Answer to Problem 90E

The required condition on b for at least one real solution is (−∞,−210]∪[210,∞) .

Explanation of Solution

Given information:

Given equation

  2x2+bx+5=0

Calculation:

As we know the real solution of a quadratic equation ax2+bx+c=0 is only possible when b2−4ac≥0 .

Therefore,

  b2−4ac≥0b2−4×2×5≥0(b−210)(b+210)≥0(−∞,−210]∪[210,∞)

Hence the required condition on b for at least one real solution is (−∞,−210]∪[210,∞)

(b)

To determine

To write: a conjecture about the interval (s) based on the values of the coefficients.

(b)

Expert Solution
Check Mark

Answer to Problem 90E

Therefore following conjecture would be possible,

  a,c>0,a,c<0,b≤−2ac,b≥2ac .

Explanation of Solution

Calculation:

As we know the real solution of a quadratic equation ax2+bx+c=0 is only possible when b2−4ac≥0 .

  b2−4ac≥0(b−2ac)(b+2ac)≥0b≤−2acb≥2ac

Therefore following conjecture would be possible,

  a,c>0,a,c<0,b≤−2ac,b≥2ac .

Previous
Chapter 2.7, Problem 89E
Next
Chapter 2, Problem 1RE

Chapter 2 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 2.1 - Prob. 1ECh. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
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Limits and Continuity; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9brk313DjV8;License: Standard YouTube License, CC-BY