Quadratic Equation Solver
Solve quadratic equations with step-by-step solutions, discriminant analysis, and graphical visualization
Equation Input
Standard Quadratic Form
A quadratic equation is in the form:
ax2 + bx + c = 0
Where:
- a is the coefficient of x² (a ≠ 0)
- b is the coefficient of x
- c is the constant term
Coefficient a
a = 1
Coefficient b
b = -3
Constant c
c = 2
x2 - 3x + 2 = 0
How to Use This Solver
Step 1: Enter coefficients a, b, and c for your quadratic equation
Step 2: Click "Solve Quadratic Equation" to find solutions
Step 3: Review step-by-step solution using quadratic formula
Step 4: Analyze discriminant and graph of the quadratic function
Solution & Results
Your Quadratic Equation
x2 - 3x + 2 = 0
Nature of Roots
Two Distinct Real Roots
Discriminant (Δ)
1
Δ = b2 - 4ac
Vertex
(1.5, -0.25)
x = -b/2a
Solutions (Roots)
Root 1 (x₁)
2
Using quadratic formula
Root 2 (x₂)
1
Using quadratic formula
Step-by-Step Solution
Step 1: Identify coefficients: a = 1, b = -3, c = 2
Step 2: Quadratic formula: x = [-b ± √(b² - 4ac)] / 2a
Step 3: Calculate discriminant (Δ): Δ = b² - 4ac = (-3)² - 4(1)(2) = 9 - 8 = 1
Step 4: Since Δ = 1 > 0, the equation has two distinct real roots.
Step 5: Calculate roots using quadratic formula:
x₁ = [3 + √1] / 2 = 2
x₂ = [3 - √1] / 2 = 1
x₁ = [3 + √1] / 2 = 2
x₂ = [3 - √1] / 2 = 1
Step 6: Calculate vertex of parabola: Vertex = (-b/2a, f(-b/2a)) = (1.5, -0.25)
Graphical Representation
Solve an equation to see the parabola graph
The graph shows the quadratic function y = ax² + bx + c. Roots are x-intercepts where y = 0.