Solving quadratic equations
Instant search for roots using a discriminant
to get the solution
Quadratic equations
📐 Solving quadratic equations with solution progress
This calculator will help you find the roots of an equation of the form ax² + bx + c = 0 through the discriminant. The tool doesn't just give the answer, but shows a detailed step-by-step solution, which is useful for checking homework.
- a - the first coefficient (cannot be equal to 0).
- b - second coefficient.
- c is a free member.
How it works (Formula)
The calculator uses the classic algorithm that is taught in 8th grade:
- First, the Discriminant (D) is calculated using the formula:
D = b² - 4ac - Next, the roots are found depending on the sign of D:
- If D > 0: two real roots.
- If D = 0: one root.
- If D < 0: there are no roots (or complex roots, if this option is enabled).
If you need to perform simple arithmetic operations, use our regular calculator.
Frequently asked questions (FAQ)
❓ Why can’t coefficient “a” be equal to zero?
If a = 0, then the term ax² disappears, and the equation turns from quadratic to linear (bx + c = 0). To solve such problems, other formulas are used.
❓ What to do if the discriminant is negative?
In the school curriculum (real numbers) the answer is “there are no roots.” However, in higher mathematics there arecomplex numbers. Our calculator can find them too - the answer will contain the imaginary unit i.
❓ How to enter fractional numbers?
Use a period or comma. For example: 2.5 or 0.5. The calculator understands both formats.