Question

Что такое дискриминант

Answer 1

Благодаря нему находят корни квадратного уравнения. формула:$b^{2}$-4ac
если дискриминант больше нуля, уравнение имеет два корня, если равен нулю - 1 корень, если меньше - нет корней

Answer 2

Выражение D=b²-4ac,где ф и b коэффициенты квадратного уравнения,а с-свободный член этого уравнение
Если D<0-нет корней
D=0 один корень
D>0 два корня

Answer 3

What is a discriminant?

The discriminant is a mathematical term used in quadratic equations to determine the nature of the solutions. In the quadratic equation ax^2 + bx + c = 0, where a, b, and c are coefficients, the discriminant is given by the formula D = b^2 - 4ac.

The discriminant can be used to determine the number and type of solutions of a quadratic equation. Here's how it works:

1. If the discriminant is greater than zero (D > 0), the quadratic equation has two distinct real solutions. 2. If the discriminant is equal to zero (D = 0), the quadratic equation has one real solution (also known as a double root). 3. If the discriminant is less than zero (D < 0), the quadratic equation has no real solutions. In this case, the solutions are complex conjugates.

By calculating the discriminant, we can gain insights into the nature of the solutions of a quadratic equation.

For example, let's consider the quadratic equation 3x^2 + 2x - 5 = 0. By comparing the coefficients, we can determine that a = 3, b = 2, and c = -5. To find the discriminant, we can use the formula D = b^2 - 4ac:

D = (2)^2 - 4(3)(-5) = 4 + 60 = 64

Since the discriminant (D) is greater than zero, we can conclude that the quadratic equation 3x^2 + 2x - 5 = 0 has two distinct real solutions.

In summary, the discriminant is a mathematical tool used to determine the nature of the solutions of a quadratic equation based on the value of the discriminant (D)