Quadratic Equations

Quadratic Equations - Problem Solving


If the roots of ax2+bx2=0ax^2+bx-2 =0 are 1±33\frac{1\pm\sqrt{3}}{3}, what is a+b?

If the difference between the two roots of the equation x2mx+5=0x^2-mx+5=0 is 2,2, what is the value of m2?m^2?

If the sum of the squares of three consecutive positive integers is 509,509, 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

1x2+1x20=0?\frac{1}{x^2} + \frac{1}{ x} -20 = 0?


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