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Quadratic Equation Calculator
Solve for x in the equation: ax² + bx + c = 0
Enter values and click 'Calculate'.
Frequently Asked Questions
A quadratic equation is a polynomial equation of the second degree, meaning it contains at least one term in which the variable is squared but no term with a higher power. The general form is ax² + bx + c = 0, where 'x' is the variable, and 'a', 'b', and 'c' are coefficients (with 'a' not equal to 0).
Quadratic equations can be solved using several methods: factoring, completing the square, or using the quadratic formula. This calculator uses the quadratic formula: x = [-b ± sqrt(b² - 4ac)] / 2a. The term (b² - 4ac) is called the discriminant, which determines the nature of the roots.
The discriminant (Δ = b² - 4ac) provides insight into the nature of the roots:
- If Δ > 0: There are two distinct real roots.
- If Δ = 0: There is exactly one real root (a repeated root).
- If Δ < 0: There are two distinct complex (non-real) roots, which are conjugates of each other.
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