Question 42
It is known, that $x_1, x_2, x_3$ are distinct real numbers.
a) $x_2, x_3$ are zeros of the function $f_1(x) = x^2 + p_1x + q_1$; $x_3, x_1$ are zeros of the function $f_2(x) = x^2 + p_2x + q_2$; $x_1, x_2$ are zeros of the function $f_3(x) = x^2 + p_3x + q_3$. Does the function $f(x) = f_1(x) + f_2(x) + f_3(x)$ always have zeros?
b) $x_2, x_3$ are zeros of the function $f_1(x) = a_1x^2 + b_1x + c_1$; $x_3, x_1$ are zeros of the function $f_2(x) = a_2x^2 + b_2x + c_2$; $x_1, x_2$ are zeros of the function $f_3(x) = a_3x^2 + b_3x + c_3$. Does the function $f(x) = f_1(x) + f_2(x) + f_3(x)$ always have zeros?
a) $x_2, x_3$ are zeros of the function $f_1(x) = x^2 + p_1x + q_1$; $x_3, x_1$ are zeros of the function $f_2(x) = x^2 + p_2x + q_2$; $x_1, x_2$ are zeros of the function $f_3(x) = x^2 + p_3x + q_3$. Does the function $f(x) = f_1(x) + f_2(x) + f_3(x)$ always have zeros?
b) $x_2, x_3$ are zeros of the function $f_1(x) = a_1x^2 + b_1x + c_1$; $x_3, x_1$ are zeros of the function $f_2(x) = a_2x^2 + b_2x + c_2$; $x_1, x_2$ are zeros of the function $f_3(x) = a_3x^2 + b_3x + c_3$. Does the function $f(x) = f_1(x) + f_2(x) + f_3(x)$ always have zeros?