Quadratic Equation Solver
A quadratic equation has the form ax² + bx + c = 0, where a is non-zero. Toolverge solves it with the quadratic formula, first computing the discriminant (b² − 4ac) to determine whether the roots are two real numbers, one repeated real number, or a complex conjugate pair, then reports the vertex and axis of symmetry of the parabola y = ax² + bx + c.
How it works
- Enter coefficients a, b, and c.
- The discriminant b²−4ac determines real, repeated, or complex roots.
- The vertex and axis of symmetry are computed from the same coefficients.
Formula x = (−b ± √(b²−4ac)) / 2a; vertex x = −b/2a
Frequently asked questions
How do I solve x²−3x+2=0?
Using the quadratic formula with a=1, b=−3, c=2 gives roots x=1 and x=2.
What does a negative discriminant mean?
It means the equation has no real roots — the two roots are a complex conjugate pair.
What is the vertex of a parabola?
The point where the parabola turns; its x-coordinate is −b/2a, also called the axis of symmetry.
Can a be zero?
No. If a=0 the equation is linear, not quadratic, so a must be non-zero.
What does a discriminant of zero mean?
The equation has exactly one repeated real root, and the vertex touches the x-axis there.