Quadratic Equation Solver
Solve equations of the form ax² + bx + c = 0
a
b
c
x² – 3x + 2 = 0
Solution
Two Real Solutions
Discriminant (Δ)
1
The discriminant (Δ = b² – 4ac) determines the nature of the roots:
- Δ > 0: Two distinct real roots
- Δ = 0: One real double root
- Δ < 0: Two complex conjugate roots
Solutions
- x₁ = 2
- x₂ = 1
These are the values of x that satisfy the equation.
Solution Steps
- Equation: ax² + bx + c = 0 with a=1, b=-3, c=2
- Calculate discriminant: Δ = b² – 4ac = (-3)² – 4×1×2 = 9 – 8 = 1
- Since Δ > 0, there are two real solutions
- Calculate solutions: x = [-b ± √Δ] / (2a)
- x₁ = [3 + √1] / 2 = 4 / 2 = 2
- x₂ = [3 – √1] / 2 = 2 / 2 = 1