Polynomial Function Calculator Given Zeros

Zeros of Polynomial Calculator

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

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

Zeros of a Polynomial

\( a \) is a nix of a polynomial \( P(x) \) if and only if \( P(a) = 0 \)
or
\( a \) is a nothing of a polynomial \( P(10) \) if and but if \( x - a \) is a factor of \( P(x) \)
Note that the zeros of the polynomial \( P(ten) \) refer to the values of \( x \) that makes \( P(x) \) equal to cypher. But both the zeros and the roots of a polynomial are establish using factoring and the cistron theorem [ane ii].

Example
Notice the zeros of the polynomial \( P(x) = x^2 + 5x - 14 \).
Solution
Factor \( P(x) \) as follows
\( P(ten) = (ten-two)(x+seven) \)
Set \( P(x) = 0 \) and solve
\( P(x) = (x-two)(x+vii) = 0 \)
Apply the gene theorem [1 2] and write that each cistron is equal to zero.
\( x-2 = 0 \) or \( 10+7 = 0 \)
Solve to obtain
\( x = two \) and \( 10 = - 7 \)
Hence the zeros of \( P(ten) \) are \( x = 2 \) and \( x = - seven \)

Employ of the zeros Calculator

1 - Enter and edit polynomial \( P(10) \) and click "Enter Polynomial" then cheque what y'all accept entered and edit if needed.
Note that the 5 operators used are: + (plus) , - (minus), , ^ (ability) and * (multiplication). (case: P(x) = -two*x^4+viii*x^iii+14*x^2-44*10-48).(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 have a large amount of time to be computated and their expressions may be quite complicated to understand.

Notes: In editing functions, use the following:
ane - The five operators used are: + (plus) , - (minus), / (sectionalization) , ^ (power) and * (multiplication). (instance: P(x) = 2*x^2 - 2*x - four )
Here are some examples of polynomials that you may copy and paste to exercise:
x^2 - ix ten^2 + nine 10^2 + 2*x + 7 x^three + 2*10 - 3 three*x^4 - 3
x^v+5*x^4+three*x^3+x^two-10*10-120 x^5+4x^4-7x^3-28x^2+6x+24
x^4 - 4*x^3 + 3 (this 1 has very complicated zeros and takes time to compute; try information technology to have an thought.)