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Zeros Calculator

Write down your function in the designated field, and the tool will find the zeros (real, complex) for it, with their sum and product displayed.

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Zeros Calculator

The Zeros Calculator determines the zeros (exact, numerical, real, or complex) of functions over a given interval. This tool works with linear, quadratic, polynomial, cubic, rational, irrational, quartic, exponential, logarithmic, trigonometric, hyperbolic, and absolute value functions.

What are Zeros of a Function?

In mathematics, the zeros of a function f(x) are the values of x in its domain for which f(x) = 0. These points are also called roots of the function. For a polynomial, the zeros are the values of the variable that make the polynomial equal to zero.

Zeros Formula

For a linear polynomial P(x) = mx + n, the zero is found by setting P(x) = 0:

P(k) = mk + n = 0
k = -n / m

Example: If P(x) = 9x + 15, then:

9k + 15 = 0
k = -15 / 9 = -5/3

How to Find Zeros of a Function

Set the function equal to zero: f(x) = 0.
Solve for x, isolating the variable.
Check for all possible solutions depending on the function type (linear, quadratic, polynomial, etc.).

Example 1:

Find the value of 'a' if the degree of the function x³ + m^(a-4) + x² + 1 is 10.

Solution:

The degree is determined by the highest exponent. Set a - 4 = 10 → a = 14.

Example 2:

Calculate the zeros, sum, and product of the quadratic function 4x² - 9.

Solution:

Factor the quadratic:

4x² - 9 = (2x + 3)(2x - 3)

Set each factor to zero:

2x + 3 = 0 → x = -3/2
2x - 3 = 0 → x = 3/2

Zeros of the function: x = -3/2, 3/2

Zero Sum = (-3/2) + (3/2) = 0

Zero Product = (-3/2) * (3/2) = -9/4

How This Zeros Calculator Works

Input:

Enter an equation or function for which you want to find zeros.
Click the "Calculate" button.

Output:

Exact and real values of zeros
Sum and product of all roots

Reference

Wikipedia: Zero of a function – Polynomial roots, Fundamental theorem of algebra, Zero set.

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