Effortlessly find the zeros (roots) of any quadratic function. This calculator solves for the x-intercepts where the function equals zero, providing step-by-step mathematical breakdowns.
Find Zeros Calculator
Enter coefficients for: ax² + bx + c = 0
Find Zeros Calculator Formula
Reference: Khan Academy – Quadratic Formula
Variables:
- a: The quadratic coefficient (must not be zero).
- b: The linear coefficient.
- c: The constant term.
What is a Find Zeros Calculator?
A “find zeros calculator” is a specialized tool used to determine the values of x for which a function f(x) equals zero. In the context of algebra, these are also known as the roots or x-intercepts of the equation.
For quadratic functions, finding zeros helps in graphing parabolas, determining projectile motion landing points, and solving optimization problems in physics and economics.
How to Calculate Zeros (Example)
Suppose you have the equation: x² – 5x + 6 = 0
- Identify variables: a = 1, b = -5, c = 6.
- Calculate the discriminant: D = (-5)² – 4(1)(6) = 25 – 24 = 1.
- Since D > 0, there are two real zeros.
- Apply formula: x = [5 ± √1] / 2.
- Result: x₁ = 3, x₂ = 2.
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Frequently Asked Questions (FAQ)
If b² – 4ac < 0, the zeros are "complex" or "imaginary," meaning the graph never touches the x-axis.
No. If ‘a’ is zero, the equation becomes linear (bx + c = 0), not quadratic.
Yes, in mathematical terminology, the zeros of a function are the roots of the corresponding equation.
A quadratic function can have 0, 1, or 2 real zeros.