Question

Существует ли квадратичный трёхчлен, который при x=2014;2015;2016 принимает значения 2015;0;2015 соответственно? . Помогите пожалуйста буду оооооооооочень благодарен.. Срочно нужно решение! :C

Answer 1

Да, существует.

Рассмотрим функцию f(x)=2015(x-2015)². Легко видеть. что она является квадратным трехчленом и что f(2014)=2015*(-1)²=2015, f(2015)=0, f(2016)=2015*1²=2015.

Answer 2

Quadratic Polynomial with Specific Values

To determine if there exists a quadratic polynomial that takes the values 2015, 0, and 2015 when x is equal to 2014, 2015, and 2016 respectively, we can use the general form of a quadratic polynomial:

f(x) = ax^2 + bx + c

We can substitute the given values of x and the corresponding function values into the equation to form a system of equations:

1. When x = 2014, f(x) = 2015: 2015 = a(2014)^2 + b(2014) + c

2. When x = 2015, f(x) = 0: 0 = a(2015)^2 + b(2015) + c

3. When x = 2016, f(x) = 2015: 2015 = a(2016)^2 + b(2016) + c

We can solve this system of equations to find the values of a, b, and c. However, it is important to note that the given values of x and the corresponding function values are not consistent. Therefore, it is not possible to find a quadratic polynomial that satisfies all three conditions simultaneously.

Conclusion: There is no quadratic polynomial that takes the values 2015, 0, and 2015 when x is equal to 2014, 2015, and 2016 respectively.