📐 Math
Quadratic Formula Calculator
Solve quadratic equations using the quadratic formula, with step-by-step solutions for real and complex roots.
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Formula
x = (-b ± √(b² - 4ac)) / 2aa- Coefficient of x² (a ≠ 0)
b- Coefficient of x
c- Constant term
Example
Solving a Quadratic Equation
Find the roots of the equation 2x² - 5x - 3 = 0.
- Identify coefficients: a = 2, b = -5, c = -3.
- Calculate the discriminant (Δ = b² - 4ac): (-5)² - 4(2)(-3) = 25 + 24 = 49.
- Since Δ > 0, there are two real roots.
- Apply the formula: x = (5 ± √49) / 4 = (5 ± 7) / 4.
- Root 1: (5 + 7) / 4 = 12 / 4 = 3.
- Root 2: (5 - 7) / 4 = -2 / 4 = -0.5.
Frequently Asked Questions
The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a. It is used to find the solutions to any quadratic equation of the form ax² + bx + c = 0.
The discriminant is the part of the formula under the square root: b² - 4ac. It determines how many and what type of roots the equation has.
Yes. If the discriminant is negative, the calculator will find the complex roots involving imaginary numbers (i).