Quadratic Equation Solver
Solve equations in the form ax² + bx + c = 0
Solution:
Understanding Quadratic Equations
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' are known numbers, with 'a' ≠ 0. If 'a' = 0, the equation is linear, not quadratic.
The Quadratic Formula
To find the roots (solutions) of the equation, we use the quadratic formula:
x = (-b ± √(b² – 4ac)) / 2a
The part inside the square root (b² – 4ac) is called the discriminant. It tells us how many real solutions the equation has.
Types of Roots
- Discriminant > 0: Two distinct real roots.
- Discriminant = 0: One real root (a repeated root).
- Discriminant < 0: Two complex roots (involving imaginary numbers).