Quadratic Equation Solver
Solve quadratic equations (ax² + bx + c = 0) with step-by-step solutions. Shows discriminant, roots, and vertex form.
Quadratic Equation: ax² + bx + c = 0
x² +x += 0
Solution
Discriminant (b² - 4ac)
1
Positive: two real roots
Root Type
Two distinct real roots
x1 =3
x2 =2
Vertex Point
(2.5, -0.25)
Vertex Form
y = (x - 2.5)² - 0.25
Step-by-Step Solution
Step 1: Identify coefficients: a = 1, b = -5, c = 6
Step 2: Calculate the discriminant: D = b² - 4ac = (-5)² - 4(1)(6) = 25 - 24 = 1
Step 3: Apply the quadratic formula: x = (-b ± √D) / (2a)
x = (-(-5) ± √1) / (2 × 1)
x = (5 ± 1) / 2
x1 = 3
x2 = 2
Step 4: Vertex: x = -b/(2a) = 5/2 = 2.5
y = 1(2.5)² + -5(2.5) + 6 = -0.25