Question 834607
The discriminant *[tex \Delta] of a quadratic in the form *[tex ax^2 + bx + c = 0], where a, b, c are reals, is *[tex \Delta = b^2 - 4ac].

If *[tex \Delta > 0], the quadratic has two distinct real roots.

If *[tex \Delta = 0], the quadratic has one real double root.

If *[tex \Delta < 0], the quadratic has two distinct non-real roots.

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For example, the discriminant of *[tex x^2 + 2x + 5] is *[tex \Delta = 2^2 - 4(1)(5) = -16 < 0]. So the quadratic has two distinct non-real roots.