Complex Roots: How A Negative Discriminant Impacts Quadratic Equations

If b²-4ac = 0

1 real root

If b²-4ac = 0, it means that the quadratic equation of the form ax² + bx + c = 0 has equal roots. In other words, the roots of the equation would be the same. This can be seen by using the quadratic formula, which gives the roots of the equation:

x = (-b ± √(b²-4ac)) / 2a

When b²-4ac = 0, the term inside the square root becomes 0, resulting in only one root, given by:

x = -b / 2a

This root is repeated twice, hence the equal roots of the equation.

Geometrically, this means that the quadratic equation represents a parabola that just touches the x-axis at one point. This point of contact is where the roots of the equation are located.

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