/*! 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 155 What is the discriminant and wha... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 155

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

Short Answer

Expert verified
The discriminant in a quadratic equation is the expression under the square root in the quadratic formula (鈭� = B虏 - 4AC). It provides information about the roots of a quadratic equation. If 鈭� is positive, there are two distinct real roots, if it equals to zero, there's one real (repeated) root and if it's negative, there are two complex roots.

Step by step solution

01

Discriminant Definition

The discriminant refers to the term \( \Delta = B^2 - 4AC \) under the square root in the quadratic formula used to find the solutions of a quadratic equation in the form of \( Ax^2 + Bx + C = 0 \), where A, B and C are constants and A 鈮� 0.
02

The Significance of the Discriminant Value

The value of the discriminant (螖) gives information about the roots of a quadratic equation. If 螖 > 0, the equation has two distinct real roots. If 螖 = 0, the equation has one real root (or a repeated root.) If 螖 < 0, the equation has two complex roots.
03

Example

Consider the quadratic equation \( x^2 - 5x + 6 = 0 \). Here, A = 1, B = -5, and C = 6. We calculate the discriminant as: \( \Delta = B^2 - 4AC = (-5)^2 - 4*1*6 = 25 - 24 = 1 \) which is greater than zero. Hence, the given quadratic equation has two distinct real roots.

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

A new car worth \(\$ 24,000\) is depreciating in value by \(\$ 3000\) per year. a. Write a formula that models the car's value, \(y,\) in dollars, after \(x\) years. b. Use the formula from part (a) to determine after how many years the car's value will be \(\$ 9000\).

In 2014 , the average price of a new car was \(\$ 37,600\). For the period shown, new-car prices increased by approximately \(\$ 1250\) per year. If this trend continues, how many years after 2014 will the price of a new car average \(\$ 46,350 ?\) In which year will this occur?In \(2014,\) the average age of cars on U.S.roads was 11.3 years. For the period shown, this average age increased by approximately 0.2 year per year. If this trend continues, how many years after 2014 will the average age of vehicles on U.S. roads be 12.3 years? In which year will this occur?

List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational mumbers, f. real numbers. $$\left\\{-9,-\frac{4}{5}, 0,0.25, \sqrt{3}, 9.2, \sqrt{100}\right\\}$$

State the name of the property illustrated. $$-8(3+11)=-24+(-88)$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When performing the division $$\frac{7 x}{x+3}+\frac{(x+3)^{2}}{x-5}$$ I began by dividing the numerator and the denominator by the common factor, \(x+3\).
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

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.