Quadratic Formula Calculator
Calculate the roots of a quadratic equation using the quadratic formula. Find both real and complex solutions for any quadratic equation in the form ax² + bx + c = 0.
Category: Math
Quadratic Formula Calculator
Enter the coefficients for the equation ax² + bx + c = 0
Frequently Asked Questions
What is the quadratic formula?
The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), which gives the solutions to the quadratic equation ax² + bx + c = 0, where a, b, and c are coefficients and a ≠ 0. It can find both real and complex roots.
What is the discriminant in a quadratic equation?
The discriminant is the expression b² - 4ac in the quadratic formula. It determines the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root (a double root); if negative, there are two complex conjugate roots.
Can all quadratic equations be solved using the quadratic formula?
Yes, all quadratic equations can be solved using the quadratic formula, provided they are in the standard form ax² + bx + c = 0 and a ≠ 0. This formula works even when the roots are complex numbers.
Why might I get complex solutions?
Complex solutions occur when the discriminant (b² - 4ac) is negative, making it impossible to find real number solutions. These roots appear in the form a + bi and a - bi, where i is the imaginary unit (√-1). Complex roots are important in fields like physics, engineering, and signal processing.