Quadratic Formula Calculator
x²
+
x
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= 0
Result
Quadratic Formula
The quadratic formula is used to solve equations in the form:
ax² + bx + c = 0
The formula is:
x = (-b ± √(b² - 4ac)) / (2a)
Discriminant
The discriminant (b² - 4ac) determines the nature of the roots:
- If discriminant > 0: Two real roots
- If discriminant = 0: One real root (double root)
- If discriminant < 0: Two complex conjugate roots
Example Problems
Example 1: x² + 5x + 6 = 0
Step 1: Identify coefficients
- a = 1
- b = 5
- c = 6
Step 2: Calculate discriminant
b² - 4ac = 25 - 24 = 1
Step 3: Apply quadratic formula
x = (-5 ± √1) / 2
Solutions: x = -2 or x = -3
Example 2: 2x² - 4x + 2 = 0
Step 1: Identify coefficients
- a = 2
- b = -4
- c = 2
Step 2: Calculate discriminant
b² - 4ac = 16 - 16 = 0
Step 3: Apply quadratic formula
x = (4 ± √0) / 4
Solution: x = 1 (double root)
Vertex Form
The vertex form of a quadratic equation is:
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
To convert from standard form:
- h = -b/(2a)
- k = c - b²/(4a)
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