Real Zero Of A Function - Varsity Tutors

Home » How To Find Real Zeros » Real Zero Of A Function - Varsity Tutors

Maybe your like

Skip to main contentVarsity Tutors LogoHotMathReal Zero of a Function

Real Zero of a Function

Study Guide

Key Definition

A real zero of a function $f$ is a real number $r$ such that $f(r) = 0$.

Important Notes

  • The equation $f(x) = 0$ is used to find real zeros.
  • Real zeros are where the graph crosses the x-axis.
  • A polynomial of degree $n$ can have up to $n$ real zeros.
  • Factoring a polynomial can help find its zeros.
  • Complex zeros come in conjugate pairs, but they are not real zeros.

Mathematical Notation

$+$ represents addition$-$ represents subtraction$\times$ or $*$ represents multiplication$\div$ or $/$ represents division$\sqrt{x}$ represents the square root of $x$Remember to use proper notation when solving problems

Why It Works

The real zero of a function $f(x)$ occurs where the function equals zero, which is equivalent to solving $f(x) = 0$.

Remember

To find real zeros, solve $f(x) = 0$.

Quick Reference

Quadratic Formula:$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Understanding Real Zero of a Function

Choose your learning level

Watch & Learn

Video explanation of this concept

concept. Use space or enter to play video.concept thumbnailBeginner

Start here! Easy to understand

BeginnerIntermediateAdvanced

Beginner Explanation

A real zero is where a function $f(x)$ crosses the x-axis, meaning $f(x) = 0$.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

What are the real zeros of $f(x) = x^2 - 3x + 2$?

A$1, 2$B$-1, -2$C$0, 3$D$2, 3$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

A skateboard ramp follows a quadratic path. Find the x-coordinates where $y = 0$ for the ramp described by $y = x^2 - 2x - 8$.Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Consider a cubic function $f(x) = x^3 - 6x^2 + 11x - 6$. Find its real zeros.

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

What are the zeros of $f(x) = x^3 - x^2 - x + 1$?

A$-1, 1$B$-1, 0, 1$C$1, -1, 1$D$0, 1, 2$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

Watch & Learn

Review key concepts and takeaways

recap. Use space or enter to play video.recap thumbnail

Tag » How To Find Real Zeros