Pythagorean theorem
Find a missing side in a right triangle. Choose whether the missing side is the longest hypotenuse or one of the two perpendicular legs.
MAKE THE FORMULA CLEAR
Quadratic equation
Solve a quadratic arranged as a*x^2 + b*x + c = 0. Move all terms to the left before entering the coefficients.
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Two real roots
x1 = 3；x2 = 2
The coefficient a cannot be 0. Only real roots are shown; no real roots does not mean a program error.
Worked steps
- 1x² ＋ (-5)x ＋ (6)＝0
- First divide all coefficients by 6; discriminant b² − 4ac = 0.027778
- x = (−b ± √discriminant) / 2a
Calculates real roots of ax² + bx + c = 0. The coefficient a cannot be zero. A negative discriminant means no real roots; this version does not list complex roots.
Method and scope
The discriminant is b squared minus 4*a*c. Real roots use (-b plus or minus the square root of the discriminant) divided by 2*a.
A zero discriminant gives one repeated real root. A negative discriminant means there are no real roots, not that the tool has failed.
Coefficient a must not be zero because that would be a linear equation. This version does not display complex roots; numeric roots may be approximate.
What this helps you do
Solve a quadratic arranged as a*x^2 + b*x + c = 0. Move all terms to the left before entering the coefficients.
What to enter
Start with coefficient a of x squared, then fill the other relevant fields in the units shown. The field hints explain the required format and examples.
How the calculation works
The discriminant is b squared minus 4*a*c. Real roots use (-b plus or minus the square root of the discriminant) divided by 2*a.
Worked example
For x^2 - 5x + 6 = 0, enter 1,-5,6 in the three coefficient fields. The real roots are 2 and 3, each of which makes the original equation equal zero.
Understanding the answer
A zero discriminant gives one repeated real root. A negative discriminant means there are no real roots, not that the tool has failed.
Scope and limitations
Coefficient a must not be zero because that would be a linear equation. This version does not display complex roots; numeric roots may be approximate.