In mathematics, the triangle is the pronunciation of the fourth Greek letter Delta, which is capitalized as δ and lowercase as δ. In mathematics or physics, the capitalized δ is used to represent the incremental symbol. And lowercase δ is usually used to represent variables or symbols in higher mathematics. In algebra, δ is used as a discriminant to represent the root of a quadratic equation with one variable. That is delta = b? -4ac .

The discriminant of roots is a formula for judging the number of real roots of an equation, which is widely used in solving problems, involving the range of solution coefficients, judging the number and distribution of roots of an equation and so on. The discriminant of the root of the unary quadratic equation ax 2+bx+c = 0 (a ≠ 0) is b 2-4ac, which is expressed by "δ" (pronounced as "δ").

Extended data:

Discriminant formula of quadratic equation with one variable

Any unary quadratic equation can be matched, because the sign of a≠0, in the sense of square root, can determine the root of unary quadratic equation.

The discriminant called the root of a quadratic equation with one variable is expressed by "delta" (pronounced "delta"), that is, △ =.

Second, the discriminant of univariate cubic equation

In the special form of unary cubic equation AX 3+BX+C = 0, what is the discriminant? . At that time, there was a real root and two complex roots; At that time, there were three real roots, at that time, there was a triple zero root, and at that time, two of the three real roots were equal; There are three unequal real roots.

In the general form of unary cubic equation AX 3+BX 2+CX+D = 0, the method of judging gold content is generally adopted, namely

Order.

When A=B=0, the equation has triple real roots.

When δ = B2-4ac >; 0, the equation has a real root and a pair of * * * yoke imaginary roots.

When δ = B2-4ac = 0, the equation has three real roots, one of which is a multiple root.

When δ = B2-4ac

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