For the following two (02) items:
Let $f(x) = a x ^ 2 + bx + c$ be a quadratic polynomial such that f(1) = f(4) = 2 Further, 2 is a root of f(x) = 0

What is (a + b + c) equal to?

If one root of the equation $x{}^2-kx+k=0$ exceeds the other by $2\sqrt{3}$ then which one of the following is a value of k?

 If $x+\frac{5}{y}=4$, and then $\$y+\backslash frac\{5\}\{x\}=\; -4\$$  what is (x + y) equal to?

 If $x{}^2-x+1=0$, then what is $(x-\frac{1}{x})^2+(x-\frac{1}{x})^4+(x-\frac{1}{x})^8$