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Algebra

# Quadratic Equations - Problem Solving

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?

In the above image, the blue picture is 3 inches longer than it is wide. On all sides, the yellow frame is 5 inches around. If the area of the picture is 378, what is the area of the frame?

What are the roots of the equation

$\frac{1}{x^2} + \frac{1}{ x} -20 = 0?$

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