Roots and discriminant of any quadratic

For ax² + bx + c = 0, the quadratic formula x = (−b ± √(b²−4ac)) ÷ 2a gives the roots, and the discriminant b² − 4ac announces their nature before you compute: positive means two real roots, zero one repeated root, negative a complex pair. For x² − 5x + 6 = 0 the discriminant is 1 and the roots are 2 and 3.

Enter a, b, and c with their signs — the most common homework error is dropping a minus on b or c. Read the discriminant first: it tells you whether to expect two crossings, one touch, or no real roots, which doubles as a check on the arithmetic. With a = 0 the equation is linear, not quadratic, and the page says so instead of dividing by zero.

It does not show step-by-step working, plot the parabola, or solve cubics and higher — it returns roots plus discriminant for quadratics only, with complex pairs reported as text.

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