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Ubify Financial Advisory Board
FINANCIAL ANALYSTS & CPA REVIEWERS
About This Tool
Solve second-degree algebraic equations using the standard quadratic formula x = (-b ± √(b² - 4ac)) / (2a). Enter quadratic coefficients a, b, and c to compute radical components, discriminant evaluations, and both roots. If coefficient a equals zero, the solver identifies the expression as a linear equation and computes the single linear intercept.
How to Use
- 1
Enter quadratic coefficient a, linear coefficient b, and constant term c into the respective inputs.
- 2
Examine the radical expression b² - 4ac to inspect real versus imaginary solution sets.
- 3
View individual roots x₁ and x₂ alongside symmetry axis coordinates and radical breakdowns.
Frequently Asked Questions
What is the quadratic formula and when is it applied?
The formula x = (-b ± √(b² - 4ac)) / (2a) solves any quadratic equation ax² + bx + c = 0 where a ≠ 0, providing exact algebraic solutions regardless of whether the polynomial can be easily factored.
What is a worked numerical example using the formula?
For equation x² + 2x - 8 = 0, coefficients are a = 1, b = 2, and c = -8. The discriminant is 2² - 4(1)(-8) = 4 + 32 = 36. Applying the formula: x = (-2 ± √36)/2 = (-2 ± 6)/2, yielding roots x₁ = 2 and x₂ = -4.
What happens when the discriminant is negative?
When b² - 4ac < 0, the square root involves a negative radicand, resulting in a conjugate pair of complex numbers expressed as real ± imaginary·i.
Does this calculator transmit polynomial inputs over the internet?
No. All radical computations and floating-point divisions execute strictly within your client-side browser engine.