Solve equations in the form ax² + bx + c = 0
Your Equation:
x² + 0x + 0 = 0
📊 Solutions
Discriminant (Δ = b² - 4ac):
0
Two Real Solutions
Vertex of Parabola:
(0, 0)
📝 Step-by-Step Solution
📐 Quadratic Formula
x = (-b ± √(b² - 4ac)) / 2a
Where:
• a, b, c are coefficients from ax² + bx + c = 0
• Δ (discriminant) = b² - 4ac
• The ± symbol means there are usually two solutions
• a, b, c are coefficients from ax² + bx + c = 0
• Δ (discriminant) = b² - 4ac
• The ± symbol means there are usually two solutions
💡 Understanding the Discriminant:
- Δ > 0: Two distinct real solutions (parabola crosses x-axis twice)
- Δ = 0: One repeated real solution (parabola touches x-axis once)
- Δ < 0: Two complex solutions (parabola doesn't cross x-axis)
📚 Examples to Try:
- x² - 5x + 6 = 0 → a=1, b=-5, c=6 (Solutions: x=2 and x=3)
- x² - 4x + 4 = 0 → a=1, b=-4, c=4 (One solution: x=2)
- 2x² + 3x - 2 = 0 → a=2, b=3, c=-2 (Solutions: x=0.5 and x=-2)
- x² + x + 1 = 0 → a=1, b=1, c=1 (Complex solutions)