Quadratic Equation Solver
Algebra
Intro: Enter a quadratic like $2x^2-5x-3=0$. We show discriminant, factoring when possible, and derive solutions with exact and decimal forms.
Worked example
- Solve $\;3x^2-4x-7=0$
- Identify $a=3, b=-4, c=-7$. Discriminant $\Delta=b^2-4ac=(-4)^2-4(3)(-7)=16+84=100$.
- Since $\Delta>0$ and a perfect square, two rational roots exist.
- Quadratic formula: $x=\dfrac{-b\pm\sqrt{\Delta}}{2a}=\dfrac{4\pm10}{6}$.
- Roots: $x=\dfrac{14}{6}=\dfrac{7}{3}$ and $x=\dfrac{-6}{6}=-1$.
- Factorization check: $3x^2-4x-7=3(x+1)(x-\tfrac{7}{3})$ → expanded gives original polynomial ✔️.
- Graph note: Upward parabola (a>0) crossing x-axis at $-1$ and $\tfrac{7}{3}$; axis of symmetry $x=\tfrac{-b}{2a}=\tfrac{4}{6}=\tfrac{2}{3}$.
FAQs
Do you show completing the square?
Yes—we can transform to vertex form with full steps.
Why choose MathGPT?
- Get clear, step-by-step solutions that explain the “why,” not just the answer.
- See the rules used at each step (power, product, quotient, chain, and more).
- Optional animated walk-throughs to make tricky ideas click faster.
- Clean LaTeX rendering for notes, homework, and study guides.
How this calculator works
- Type or paste your function (LaTeX like
\sin,\lnworks too). - Press Generate a practice question button to generate the derivative and the full reasoning.
- Review each step to understand which rule was applied and why.
- Practice with similar problems to lock in the method.