Quadratic Equation Solver

About Quadratic Equation Solver

Quadratic Equation Solver computes the roots of any equation in the form ax² + bx + c = 0. Enter coefficients a, b, and c to see the discriminant, both roots (real or complex), and the step-by-step quadratic formula. The tool also shows the vertex of the parabola and whether it opens upward or downward. When the discriminant is positive, the parabola crosses the x-axis at two distinct points. When it equals zero, the parabola just touches the x-axis at one point (the vertex). When it is negative, the parabola does not cross the x-axis and the roots are complex numbers displayed in the form p + qi and p - qi. The vertex coordinates show the minimum or maximum of the parabola, which is useful in optimization problems.

How to use Quadratic Equation Solver

  1. Enter coefficients a, b, and c for ax² + bx + c = 0
  2. See the discriminant and both roots instantly
  3. Review vertex coordinates and parabola direction

Frequently Asked Questions

What is the quadratic formula?
The quadratic formula is x = (-b ± √(b²-4ac)) / 2a. It gives the roots of any quadratic equation ax² + bx + c = 0 where a is not zero.
What is the discriminant?
The discriminant is b²-4ac. If it is positive, there are two distinct real roots. If it equals zero, there is one repeated real root. If it is negative, the equation has two complex conjugate roots.
How are complex roots shown?
Complex roots are displayed as p + qi and p - qi, where p is the real part and q is the imaginary part. For example, 2 + 3i and 2 - 3i.
What happens if the discriminant is zero?
When the discriminant (b² - 4ac) equals zero, the quadratic equation has exactly one real root, called a repeated or double root. The parabola just touches the x-axis at one point, which is also the vertex of the parabola.
How do I enter a quadratic equation with no b or c term?
Enter 0 for any coefficient that is missing. For x² - 9 = 0, enter a=1, b=0, c=-9. For x² + 4x = 0, enter a=1, b=4, c=0. The calculator handles all valid quadratic equations where a is not zero.
Is Quadratic Equation Solver free and private?
Yes. Quadratic Equation Solver is completely free with no account required. All calculations run in your browser and nothing is uploaded or stored.
Does Quadratic Equation Solver work on mobile?
Yes. Quadratic Equation Solver is fully responsive and works in all modern browsers on desktop, mobile, and tablet.

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