Quadratic Equation Solver
Solve equations in the form ax² + bx + c = 0
What is a Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x, with the standard form:
ax² + bx + c = 0
Where 'x' represents an unknown variable, and 'a', 'b', and 'c' represent known numbers, with 'a' ≠ 0. If 'a' were 0, the equation would be linear, not quadratic.
The Quadratic Formula
To find the roots (solutions) of the quadratic equation, we use the quadratic formula:
x = (-b ± √(b² – 4ac)) / 2a
The part of the formula inside the square root (b² – 4ac) is called the discriminant. The value of the discriminant tells us how many real roots the equation has.
Understanding the Discriminant
- Discriminant > 0: There are two distinct real roots.
- Discriminant = 0: There is exactly one real root (a repeated root).
- Discriminant < 0: There are no real roots; instead, there are two complex roots involving imaginary numbers.
How to Use This Calculator
Simply enter the numerical values for coefficients a, b, and c into the input fields above. Ensure that 'a' is not zero. Click the "Calculate Roots" button to see the values of x that satisfy the equation.