/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 160 What is the discriminant and wha... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 160

What is the discriminant and what information does it provide about a quadratic equation?

Short Answer

Expert verified
The discriminant is part of the quadratic formula, given by \(b^2 - 4ac\), where 'a', 'b', 'c' are coefficients of the quadratic equation written in standard form \(ax^2 + bx + c = 0\). It provides information about the nature of the roots of the quadratic equation. If the discriminant is greater than zero, the equation has two distinct real roots. If it's equal to zero, there is one real root. If it's less than zero, there are two complex roots.

Step by step solution

01

Understanding the Discriminant

The discriminant is given by the formula \(b^2 - 4ac\). It can be used to analyze the roots of a quadratic equation. It does not give the actual roots of the equation, but instead, provides information about the nature of these roots.
02

Identifying the Type of Roots Using Discriminant

If the discriminant is greater than zero (\(b^2 - 4ac > 0\)), the quadratic equation will have two distinct real roots. If the discriminant is equal to zero (\(b^2 - 4ac = 0\)), the equation will have exactly one real root (or a repeated real root). If the discriminant is less than zero (\(b^2 - 4ac < 0\)), the equation will not have any real roots but two complex roots.
03

The Role of Discriminant in Quadratic Formula

The discriminant is a vital component of the quadratic formula, \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). The term \(\sqrt{b^2 - 4ac}\) under the square root sign is the discriminant, and the nature of roots (real or complex) are determined by whether it's positive, zero, or negative respectively.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve absolute value inequality. \(|2 x-6|<8\)

Describe ways in which solving a linear inequality is different than solving a linear equation.

Use the graph of \(y-|4-x|\) to solve each inequality. \(|4-x| \geq 5\)

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(\frac{x-4}{6} \geq \frac{x-2}{9}+\frac{5}{18}\)

Solve absolute value inequality. \(-2|x-4| \geq-4\)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.