Find the x-intercepts (roots) of linear and quadratic functions.
Input Coefficients
Function Roots
x₁ = 3.00, x₂ = 2.00
Function Zeros
Points where the function crosses the x-axis (f(x) = 0).
Discriminant (Δ)1.00
Function TypeQuadratic
About this calculator
What is a Zero of a Function?
A zero of a function, also called a root or x-intercept, is a value of x for which f(x) = 0. On a graph, these are the points where the function's curve touches or crosses the horizontal x-axis.
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Pro Tips
A linear function ax + b = 0 has exactly one zero at x = -b/a.
A quadratic function can have 0, 1, or 2 real zeros depending on the discriminant.
If the discriminant is negative, the zeros are complex (imaginary).
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Fun Facts
"The Fundamental Theorem of Algebra states that a polynomial of degree n has exactly n complex zeros."
"In engineering, zeros of transfer functions determine the stability and behavior of systems."
"Finding zeros is the same as finding the 'solutions' to an equation."
Formula: For ax² + bx + c = 0, x = [-b ± √(b² - 4ac)] / 2a
