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Quadratic Equation Calculator
Enter coefficients a, b, c of ax²+bx+c=0 — the calculator returns the discriminant and roots.
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How we solve quadratic equations
Discriminant = b²−4ac. When >0: two real roots. When =0: one double root. When <0: no real roots.
Example: x²−5x+6=0
a=1, b=−5, c=6 → discriminant=1 > 0 → x1=2, x2=3.
Frequently asked questions
What is a quadratic equation?
An equation of the form ax²+bx+c=0 where a≠0. The graph is a parabola.
What is the discriminant?
Delta = b²−4ac. Its sign determines the number of real roots.
What does delta > 0 mean?
Two distinct real roots: x = (−b ± √delta) / (2a).
What does delta = 0 mean?
One repeated root (double root): x = −b / (2a).
What does delta < 0 mean?
No real roots. The parabola does not cross the x-axis (complex roots only).
What are the quadratic formula roots?
x = (−b ± √(b²−4ac)) / (2a). This works for any quadratic equation.
Can I solve by factoring?
Yes, if the equation factors nicely. Use the calculator to verify.
What is a double root?
When delta=0, both solutions are the same: x = −b/(2a). The parabola is tangent to the x-axis.
What if a = 0?
If a=0 the equation becomes linear (bx+c=0). The quadratic formula does not apply.
What are Vieta's formulas?
For roots x1 and x2: x1+x2 = −b/a and x1·x2 = c/a. Useful to verify solutions.
For educational purposes.