Quadratic Equation Calculator CA
Solve any quadratic equation ax² + bx + c = 0 — get the real or complex roots, the discriminant and the vertex.
How it works
Enter the coefficients a, b and c. The calculator applies the quadratic formula, reports whether the roots are real or complex, and also gives the discriminant and the vertex of the parabola.
Frequently asked questions
What is the quadratic formula?
x = (−b ± √(b² − 4ac)) ÷ 2a, which solves any equation of the form ax² + bx + c = 0.
What is the discriminant?
It is b² − 4ac — the part under the square root. It reveals whether the equation has two, one or no real solutions.
How many solutions does a quadratic have?
If the discriminant is positive there are two real roots, if it is zero there is one repeated root, and if it is negative there are two complex roots.
How do I solve a quadratic equation?
Identify a, b and c, then put them into the quadratic formula, or factorise if the equation factors neatly.
What if a equals zero?
Then it is not quadratic but linear (bx + c = 0), solved simply as x = −c ÷ b.
Can a quadratic have no real solutions?
Yes — if the discriminant is negative, the two solutions are complex numbers rather than real ones.
Quadratic Equation Calculator
A quadratic equation has the form ax² + bx + c = 0. This calculator finds its solutions (roots) using the quadratic formula.
The quadratic formula
x = ( −b ± √(b² − 4ac) ) ÷ 2a
The discriminant
The part under the square root, b² − 4ac, tells you how many real solutions there are: greater than 0 gives two real roots, exactly 0 gives one repeated root, and less than 0 gives two complex roots.
Worked example
For x² − 5x + 6 = 0: a=1, b=−5, c=6. The discriminant is 25 − 24 = 1, so x = (5 ± 1) ÷ 2, giving x = 3 and x = 2.
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