Quadratic Equation Solver
ax² + bx + c = 0
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About Quadratic Equations
A quadratic equation is a second-degree polynomial equation in one variable. The standard form is ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.
The solutions to a quadratic equation are found using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
The discriminant (b² - 4ac) determines the nature of the roots. Positive discriminant means two real roots, zero means one repeated root, and negative means two complex roots.
Frequently Asked Questions
A quadratic equation is a polynomial equation of degree 2, written in the form ax² + bx + c = 0, where a, b, and c are coefficients and a ≠ 0. The solutions (roots) can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a.
The discriminant (Δ = b² - 4ac) determines the nature of the roots. If Δ > 0, there are two distinct real roots. If Δ = 0, there is one repeated real root. If Δ < 0, there are two complex (imaginary) roots.
When the discriminant is negative, the quadratic equation has no real solutions. Instead, it has complex roots involving the imaginary unit 'i', where i² = -1. Complex roots always come in conjugate pairs.