# Zeros of Polynomial Calculator



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.

$P(x)$ =

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.)