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Quadratic equations describe the motion of a baseball after it connects with a bat, and the acceleration of gravity at the Earth's orbit.

If the roots of \(ax^2+bx-2 =0 \) are \(\frac{1\pm\sqrt{3}}{3}\), what is a+b?

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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?

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What are the roots of the equation

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

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