Quadratic Equation Root Calculator

How to calculate Quadratic formula calculator?

Apply the quadratic formula to the equation ax² + bx + c = 0 by first evaluating the discriminant and then substituting into the formula to get the roots.

Key formula: x = (-b ± √(b2 - 4ac)) / (2a)

Using the Quadratic formula calculator calculator: an example

Example values: a = 1, b = -3, c = 2.

Step-by-step calculation:

1. Compute the discriminant: D = b2 - 4ac = (-3)2 - 4·1·2 = 9 - 8 = 1.
2. Take the square root: √D = 1.
3. Substitute into the formula: x = ( -b ± √D ) / (2a) = (3 ± 1) / 2, giving x = 2 and x = 1.
4. Conclude the equation has two distinct real roots: x = 2 and x = 1.

Frequently Asked Questions

What if the discriminant is negative?

If the discriminant is negative there are no real roots; the quadratic has two complex conjugate roots instead.

Can coefficient a be zero?

If a = 0 the equation is linear (bx + c = 0) and not quadratic; solve it as a linear equation using x = -c/b.

What does a zero discriminant mean?

A discriminant of zero indicates one repeated real root given by x = -b / (2a); the parabola touches the x-axis at a single point.