The number of real roots for the equation $${x^2} + 9\left| x \right| + 20 = 0$$ is

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 $(x-\frac{1}{x})^2+(x-\frac{1}{x})^4+(x-\frac{1}{x})^8$