Quadratic Equations - Problem Solving Practice Problems Online

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

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

x=-4 \text{ or } x=5

x=-{5} \text{ or } x={4}

x=-\frac{1}{4} \text{ or } x=\frac{1}{5}

x=-\frac{1}{5} \text{ or } x=\frac{1}{4}

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Quadratic Equations - Problem Solving