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In algebra, the discriminant of a polynomial is a polynomial function of its coefficients, which allows deducing some properties of the roots without computing them. For example, the discriminant of the quadratic polynomial
a
x
2
+
b
x
+
c
{displaystyle ax^{2}+bx+c}
is
b
2
−
4
a
c
,
{displaystyle b^{2}-4ac,}
which is zero if and only if the polynomial has a double root, and is positive if and only if the polynomial has two real roots.