Find all zeros of the polynomial calculator

Question

\( \)\( \)\( \)\( \)

Table of Contents Show

Zeros of a Polynomial
Use of the zeros Calculator
More References and Links
Number Line
Number Line
How do you find the missing zeros of a polynomial?

A calculator to calculate the real and complex zeros of a polynomial is presented.

Zeros of a Polynomial

\( a \) is a zero of a polynomial \( P(x) \) if and only if \( P(a) = 0 \)
or
\( a \) is a zero of a polynomial \( P(x) \) if and only if \( x - a \) is a factor of \( P(x) \)
Note that the zeros of the polynomial \( P(x) \) refer to the values of \( x \) that makes \( P(x) \) equal to zero. But both the zeros and the roots of a polynomial are found using factoring and the factor theorem [1 2].

Example
Find the zeros of the polynomial \( P(x) = x^2 + 5x - 14 \).
Solution
Factor \( P(x) \) as follows
\( P(x) = (x-2)(x+7) \)
Set \( P(x) = 0 \) and solve
\( P(x) = (x-2)(x+7) = 0 \)
Apply the factor theorem [1 2] and write that each factor is equal to zero.
\( x-2 = 0 \) or \( x+7 = 0 \)
Solve to obtain
\( x = 2 \) and \( x = - 7 \)
Hence the zeros of \( P(x) \) are \( x = 2 \) and \( x = - 7 \)

Use of the zeros Calculator

1 - Enter and edit polynomial \( P(x) \) and click "Enter Polynomial" then check what you have entered and edit if needed.
Note that the five operators used are: + (plus) , - (minus), , ^ (power) and * (multiplication). (example: P(x) = -2*x^4+8*x^3+14*x^2-44*x-48).(more notes on editing functions are located below)
2 - Click "Calculate Zeros" to obain the zeros of the polynomial.
Note that the zeros of some polynomials take a large amount of time to be computated and their expressions may be quite complicated to understand.

Notes: In editing functions, use the following:
1 - The five operators used are: + (plus) , - (minus), / (division) , ^ (power) and * (multiplication). (example: P(x) = 2*x^2 - 2*x - 4 )
Here are some examples of polynomials that you may copy and paste to practice:
x^2 - 9 x^2 + 9 x^2 + 2*x + 7 x^3 + 2*x - 3 3*x^4 - 3
x^5+5*x^4+3*x^3+x^2-10*x-120 x^5+4x^4-7x^3-28x^2+6x+24
x^4 - 4*x^3 + 3 (this one has very complicated zeros and takes time to compute; try it to have an idea.)

Number Line

Graph

Hide Plot »

Sorry, your browser does not support this application

Examples

-4x^3+6x^2+2x=0
6+11x+6x^2+x^3=0
2x^5+x^4-2x-1=0
11+6x+x^2=-\frac{6}{x}
x^3-2x=0
2x^5+x^4-2x-1=0

polynomial-equation-calculator

en

Related » Graph » Number Line » Similar » Examples »

Our online expert tutors can answer this problem

Get step-by-step solutions from expert tutors as fast as 15-30 minutes. Your first 5 questions are on us!

You are being redirected to Course Hero

I want to submit the same problem to Course Hero

Correct Answer :)

Let's Try Again :(

Try to further simplify

Number Line

Graph

Hide Plot »

Sorry, your browser does not support this application

Examples

roots\:-6x^{2}+36x-59
roots\:x^{2}-x-6
roots\:x^{2}-1
roots\:x^{2}+2x+1
roots\:2x^{2}+4x-6

roots-calculator

en

How do you find the missing zeros of a polynomial?

Use the Rational Zero Theorem to list all possible rational zeros of the function. Use synthetic division to evaluate a given possible zero by synthetically dividing the candidate into the polynomial. If the remainder is 0, the candidate is a zero. If the remainder is not zero, discard the candidate.

find zeros polynomial calculator Multiplicity calculator Multiplicity Calculator polynomial