# If a function has a discriminant that is less than zero, what does this mean?

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If a quadratic function is of the form `y=ax^2+bx+c` then the discriminant is `D=b^2-4ac` .

Recall the quadratic formula -- if the quadratic is in standard form then the solutions are `x=(-b+-sqrt(b^2-4ac))/(2a)` . This implies that the solutions are `sqrt(b^2-4ac)` away from `-b/(2a)` . Graphically, if the solutions are real, then they are equidistant from the axis of symmetry `x=-b/(2a)` .

What happens when `sqrt(b^2-4ac)=0` ? The solution lies on the axis of symmetry -- thus the solution is the vertex. (This is a double root.)

What happens when `sqrt(b^2-4ac)<0` ? The left side is not real -- when you add or subtract an imaginary number from a real number you get an imaginary number. So the solutions are imaginary. Graphically, the parabola does not intersect the x-axis.

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**If the discriminant is less than zero, then the quadratic has no real solutions -- it will have two imaginary solutions.**

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