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$\large a x^2 + b x + c = 0$
$$a$$ =
$$b$$ =
$$c$$ =

The quadratic equation is an equation of the form:

$a x^2 + b x + c = 0$

with $$a \ne 0$$. It has solutions of the form

$x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$

In order to analyze the nature of the solution, the discriminant is defined as:

$D = b^2 – 4ac$

Based on the value of the discriminant, the nature of the solutions is defined. In fact, when $$D > 0$$, then there are two different real solutions, when $$D = 0$$, there is one repeated real solution, and when $$D < 0$$, there are two different imaginary solutions.