Calculate a Quadratic Equation
Calculator for quadratic equations. Both results of the equation ax²+bx+c=0 will be calculated, for variables and numbers as input values. At Enter variables, the equation can be filled with any input values, those will be inserted into the quadratic formula without calculation. At Calculate numbers, only numbers may be entered, the results will be real or complex numbers. Complex numbers will be shown as x + yi, i is the imaginary unit √-1.
The quadratic formula, which finds the results for the quadratic equation, is x1,2 = ( -b ± √ b² - 4ac ) / 2a
The values x1 and x2 are the zeroes of the parabola which is defined by the quadratic equation. Here you can draw a parabola.
Enter variables:
Here, the values a, b and c of the quadratic formula are replaced by the bracketed input values. The formula won't be solved, but the display of the input values in the quadratic formula is a helpful step to find a result.
Example Calculate numbers:
- The parabola 2x² + 3x + 1 has zeroes at -0.5 and -1.
- The parabola 2x² + 3x + 5 has no real zeroes and two complex zeros at -0.75 + 1.392 i and -0.75 + 1.392 i.
- The normal parabola x² has a double zero at 0.
Solving quadratic equations is one of the oldest problems in mathematics. It appears in the Pythagorean theorem, the earliest known writing comes from ancient Babylonia about 4000 years ago. In the fifth century B.C., it was found that some of the solutions to these equations cannot be represented as fractions, i.e. they are irrational numbers. The formulas for quadratic equations, Vieta's formulas, were finally discovered by the French mathematician François Vieta in the second half of the 16th century.