Question

Use a table to solve. $2 x^{2} \leq 1-4 x$

   Use a table to solve.
$2 x^{2} \leq 1-4 x$

College Algebra with Modeling and Visualization

College Algebra with Modeling and Visualization

Gary K. Rockswold 4th Edition

Chapter 3, Problem 60

Instant Answer

Solved by Expert Gladys Fowler

06/28/2021

Step 1

The standard form of a quadratic equation is $ax^{2} + bx + c = 0$. So, we rewrite the inequality as follows: \[2x^{2} + 4x - 1 \leq 0\] Show more…

Show all steps

lock

Thanks for your feedback!

Use a table to solve. $2 x^{2} \leq 1-4 x$

Play audio

Feedback

Powered by NumerAI

Gladys Fowler and 78 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Quadratic Inequalities

A quadratic inequality involves a quadratic expression where one side is compared to zero using inequality symbols. Solving such inequalities usually starts by rewriting the inequality in a standard form. The solution depends on finding the intervals on the real number line where the quadratic expression is either nonnegative or nonpositive, as required.

Standard Form

Rewriting the inequality in standard form (where all terms are on one side and the inequality is set against zero) is a crucial step. This transformation makes it possible to identify the roots of the quadratic equation, which are the key values that divide the number line into intervals with consistent behavior.

Critical Points

Critical points are the solutions to the corresponding quadratic equation when the expression is set equal to zero. These points are significant because they are where the quadratic function changes sign, and they become the boundaries of the intervals to be analyzed in solving the inequality.

Sign Chart/Table Analysis

The sign chart or table method is a systematic approach that involves dividing the number line based on the critical points and then testing a representative value in each interval. This analysis reveals the sign of the quadratic expression within each interval, enabling one to determine which intervals satisfy the original inequality.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later