Univariate quadratic equation: ax 2+bx+c = 0 (a ≠ 0)

Then ⊿ = b 2-4ac

If there are two equations, ⊿ = b 2-4ac ≥ 0.

Where > 0 is unequal and = 0 is equal.

⊿ Used to judge whether an equation has a real root and the location of the root.

⊿>； 0, the equation has two unequal real roots.

⊿<； 0, the equation has no real root.

⊿=0, this equation has two equal real roots.

Specific to the current topic, this equation is 3x 2-10x+k = 00 (that is, a=3, b=- 10, c=k).

So ⊿ = B2-4ac = (-10) 2-12k =100-12k.

The necessary and sufficient condition for the unequal real roots of this equation is ⊿ > 0, that is,100-12k >; 0, that is, k < 25/3-①

From the relationship between root and coefficient, it can be concluded that X 1+X2 = 10/3 and X 1 X2 = K/3.

Two identical symbols are equivalent to: x 1 x2 > 0, that is, k/3 >; 0, namely k>0-②

The necessary and sufficient conditions for an equation to have two real roots with the same sign but not equal are: 0.