Quadratic Formula Solver
Our Quadratic Formula Solver helps you quickly find the roots of any quadratic equation in the standard form ax² + bx + c = 0. Just enter the coefficients a, b, and c, and let the calculator do the work, showing both real and complex solutions.
Enter the coefficient of x² (cannot be 0).
Enter the coefficient of x.
Enter the constant term.
Our Quadratic Formula Solver helps you quickly find the roots of any quadratic equation in the standard form ax² + bx + c = 0. Just enter the coefficients a, b, and c, and let the calculator do the work, showing both real and complex solutions.
The quadratic formula is: x = [-b ± sqrt(b² - 4ac)] / 2a
For the equation 2x² + 5x - 3 = 0, we have a = 2, b = 5, and c = -3. 1. Calculate the discriminant: b² - 4ac = (5)² - 4(2)(-3) = 25 + 24 = 49. 2. Since the discriminant is positive (49 > 0), there are two distinct real roots. 3. Apply the quadratic formula: x = [-5 ± sqrt(49)] / (2*2) = [-5 ± 7] / 4. 4. The two roots are: x₁ = (-5 + 7) / 4 = 2 / 4 = 0.5, and x₂ = (-5 - 7) / 4 = -12 / 4 = -3.
A quadratic equation is a polynomial equation of the second degree, meaning the highest power of the variable is 2. It is typically written in the standard form ax² + bx + c = 0, where 'a', 'b', and 'c' are coefficients and 'a' is not equal to zero.
The discriminant is the part of the quadratic formula under the square root sign: b² - 4ac. Its value determines the nature of the roots of the quadratic equation. If positive, there are two real roots; if zero, there is one real root; if negative, there are two complex conjugate roots.
Yes, our Quadratic Formula Solver is designed to handle all types of roots, including complex conjugate roots. If the discriminant is negative, the calculator will display the solutions in the form of a + bi, where 'i' is the imaginary unit.
Quadratic Formula Solver Explained: Master Quadratic Equations
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