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 equivalently, \( x - a \) is a factor of \( P(x) \).

Example: Find the zeros of \( P(x) = x^2 + 5x - 14 \).
Factor: \( P(x) = (x-2)(x+7) \).
Set \( P(x) = 0 \): \( (x-2)(x+7) = 0 \).
Solve: \( x = 2 \) and \( x = -7 \).

Use of the Zeros Calculator

1 - Enter the polynomial \( P(x) \) in the input box and click "Enter Polynomial".
2 - Click "Calculate Zeros" to compute its zeros.

Notes:

Use operators +, -, *, /, ^ for polynomials. Example: \( P(x) = 2*x^2 - 2*x - 4 \).
Sample polynomials:

• x^2 - 9   ,   x^2 + 9   ,   x^2 + 2x + 7
• x^3 + 2x - 3   ,   3x^4 - 3
• x^5 + 5x^4 + 3x^3 + x^2 - 10x - 120   ,   x^5 + 4x^4 - 7x^3 - 28x^2 + 6x + 24
• x^4 - 4x^3 + 3 (may take longer to compute)

More References and Links

• Polynomials
• Factor Polynomials
• Find Zeros of Polynomials

References:
[1] Algebra and Trigonometry - Swokowsky Cole - 1997 - ISBN: 0-534-95308-5
[2] Algebra and Trigonometry with Analytic Geometry - R.E.Larson, R.P. Hostetler, B.H. Edwards, D.E. Heyd - 1997 - ISBN: 0-669-41723-8