Solve a quadratic equation ax² + bx + c = 0 for its roots. Enter the three coefficients.
Usage Tip
If the discriminant is a perfect square, the roots are rational and the quadratic factors neatly.
The discriminant b² − 4ac sets the number of real roots
The discriminant tells the story: positive gives two real roots, zero gives one, negative gives a complex pair.
Complex roots are shown in a ± bi form.
The vertex x-coordinate is −b ÷ 2a.
A quadratic equation has the form ax squared + bx + c = 0, and its roots are the values of x that make it true. The quadratic formula gives them as x equals minus b, plus or minus the square root of the discriminant, divided by 2a, where the discriminant is b squared minus 4ac.
The discriminant tells you what to expect. A positive value gives two different real roots, zero gives one repeated root, and a negative value gives two complex roots with no real solutions. The coefficient a cannot be zero, or the equation is not quadratic. Quadratics describe projectile motion, areas, and many optimization problems, and the roots are where the parabola crosses the x axis.