For a quadratic equation with , completing the square givesOver the complex numbers both roots exist, with a repeated root of a polynomial when the discriminant is zero. Over the real numbers the discriminant determines whether there are two distinct roots, one repeated root, or no real root.
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The quadratic formula is a mathematical formula used to find the solutions (or roots) of a quadratic equation, which is typically written in the standard form: \[ ax^2 + bx + c = 0 \] where \( a \), \( b \), and \( c \) are coefficients, and \( a \neq 0 \).
