This discriminant is derived from the root formula of the equation, because

Axe? +bx+c = 0 = = = & gt； a(x+b/2a)？ -B? /4a+c=0=== >x=[-b √(b？ -4ac)]/2a

As can be seen from the root formula, b? The result of -4ac determines whether the equation has real roots or what kind of real roots it has, so it is called b? -4ac is the discriminant of quadratic equation in one variable, and the symbol is △.

(1) When △=0, the equation has a real root (or two equal real roots).

(2) When △ < 0, the equation has no solution.

(3) When △ > 0, the equation has two unequal real roots.

According to the root formula and discriminant, Vieta theorem is deduced.

Suppose that the quadratic equation with one variable has two real roots x 1 and x2, then the relationship between these two real roots is:

x 1+x2 =[-b+ √△]/2a+[-b-√△]/2a =-b/a

x 1x 2 =[-b+ √△]/2a×[-b-√△]/2a = c/a

Of course, the first condition of the above conditions (including discriminant) is a≠0.