2 △ is called the discriminant of quadratic equation, which is pronounced as "Delta |".

Calculation: △ = b 2-4 * a * c (A, B and C are the coefficients of the quadratic term, linear term and constant term of the equation respectively) Role: Examples of judging the existence of real roots in a quadratic equation with one variable: 1, x2+2x+3 = 0 △ = 2 2-4 * 6544. The 0 equation has no real root.

2. The equation x2+2x+1= 0 △ = 22-4 *1*1= 0 has two equal real roots 3, x 2+2x- 1 = 0 △ = 2 2-4 * 65438. The 0 equation has two unequal real roots.

Extended data:

Application of discriminant of quadratic equation in one variable

(1) Solve the equation and judge the root of a quadratic equation.

It has two different types:

① The coefficients are all numbers;

② The coefficient contains letters;

③ The letters in the coefficient artificially give certain conditions.

(2) According to the root of a quadratic equation, determine the value range of letters in the equation or the relationship between letters.

(3) Discriminant is used to prove the roots of the equation (there are real roots, no real roots, two unequal real roots and two equal real roots).

App application

① Solve the quadratic equation of one variable and judge the root.

(2) According to the root of the equation, determine the value range of the undetermined coefficient.

③ Prove that the letter coefficient equation has real roots or no real roots.

④ Use the discriminant of root to judge the shape of triangle.

⑤ When judging the value of letters, the quadratic trinomial is completely flat.

⑥ Whether parabola and straight line have something in common can be judged.

Simultaneous equations.

⑦ It can be judged that there are several intersections between parabola and X axis.

parabola

When y=0, the intersection with the X axis (1), that is, if the value of X is needed, the quadratic equation of one variable must be solved.

. Visible parabola

The number of intersections with the X axis is determined by the conditions of the roots of the corresponding quadratic equation with one variable, and the conditions of the roots of the quadratic equation with one variable are determined by the signs of its discriminant. Therefore, the intersection of parabola and X axis has the following three situations:

1) when δ >; 0, parabola and x axis have two intersections. If the two roots of a quadratic equation are x 1 and x2, the coordinates of the two intersections of parabola and x axis are (X 1, 0) (0)(x2, 0).

2) When δ = 0, the parabola has a unique intersection with the X axis, and the intersection at this time is the vertex of the parabola, and its coordinate is (0).

3) When δ

⑧ Solving parabola (δ >; 0) and the distance between the two intersections of the x axis.

Pet-name ruby when a>0, parabolic opening up, and when

References:

Baidu encyclopedia-discriminant