Quadratic Discriminant

Quadratic Discriminant - Range of Solutions


How many intersection points are there between the two graphs of the functions y=2x24x,y=3x+5?y=2x^2-4x, y=3x+5?

If real numbers xx and yy satisfy the equation x2+y22x14y+50=0,x^2+y^2-2x-14y+50=0, what is the value of x+yx+y?

Consider two sets A={(x,y)y=x22x+35},B={(x,y)y=2kx1}.\begin{aligned} & A=\{(x,y) \mid y=x^2-2x+35\}, \\ & B=\{(x,y) \mid y=2kx-1\}. \end{aligned} How many integers kk satisfy AB=A \cap B=\emptyset?

Find the values of bb such that y=bxy=bx is a secant line to the curve y=2x2by=2x^2-b.

Consider the graphs of y=x2+ax5,y=2x6.y=x^2+ax-5, y=2x-6. If they intersect at only one point, what is the value of the positive number aa?


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