Question

Пересекаются ли графики функций y =3xв квадрате и y=5-2x?

Answer 1

3х² = 5 - 2х
3х² + 2х - 5 = 0
√D = √4 + 60 = 8
x = 1
x = -1⅔
это точки пересечения

Answer 2

To find if the graphs of the functions y = 3x^2 and y = 5 - 2x intersect, we need to determine if there are any common points (x, y) that satisfy both equations simultaneously.

Setting the two equations equal to each other:

3x^2 = 5 - 2x

Now we have a quadratic equation. Let's rearrange it into standard form:

3x^2 + 2x - 5 = 0

To check if there are real solutions for x in this equation, we can use the discriminant (Δ):

Δ = b^2 - 4ac

where a = 3, b = 2, and c = -5.

Δ = 2^2 - 4 * 3 * -5 Δ = 4 + 60 Δ = 64

Since the discriminant (Δ) is positive, there are two real solutions for x. Therefore, the graphs of y = 3x^2 and y = 5 - 2x intersect at two points in the Cartesian plane.