Two real roots
- Input
- a=1, b=−5, c=6
- Expected output
- x₁=3, x₂=2
Δ=1>0; roots 3 and 2.
Bhaskara quadratic formula
Quadratic Formula — Step-by-Step Solution
The quadratic formula solves any ax²+bx+c=0 (a≠0): x = (−b ± √(b²−4ac)) / (2a). The discriminant Δ determines how many real roots exist.
Derivation of the quadratic formula
- The formula is derived by completing the square in ax²+bx+c=0: divide by a, move c, add (b/2a)² to both sides and isolate x.
- Δ>0 → two real roots; Δ=0 → double root x=−b/(2a); Δ<0 → complex conjugate roots.
Examples
Double root
- Input
- a=1, b=−4, c=4
- Expected output
- x=2
Δ=0; double root 2.
Full tool FAQ
The discriminant Δ = b²−4ac determines the nature of roots: Δ>0 → two distinct real roots; Δ=0 → double root; Δ<0 → no real roots.
Frequently asked questions
Are Bhaskara and quadratic formula the same?
Yes. "Bhaskara" is the popular name in Brazil for the general quadratic formula.
Does this page replace official or professional review?
No. It helps explain the scenario and use the tool more safely, but real decisions should consider official sources, full context and qualified guidance when needed.