Algebra
Quadratic Equations
If the roots of \(ax^2+bx-2 =0 \) are \(\frac{1\pm\sqrt{3}}{3}\), what is a+b?
If the difference between the two roots of the equation \[x^2-mx+5=0\] is \(2,\) what is the value of \(m^2?\)
If the sum of the squares of three consecutive positive integers is \(509,\) what is the sum of the three integers?
What are the roots of the equation
\[\frac{1}{x^2} + \frac{1}{ x} -20 = 0?\]