How do you use the discriminant to determine the nature of the solutions given 2x^2+4x+3=0?

1 Answer
Tony B
Jun 17, 2016

See explanantion

Explanation:

Consider the standard form y=ax^2+bx+c

where x=(-b+-sqrt(b^2-4ac))/(2a)

The discriminant is: b^2-4ac

If b^2-4ac=0 then the curve is such that the x-axis forms a tangent to the vertex.

If b^2-4ac>0 then the curve crosses the x-axis and there are two solutions to y=0

If b^2-4ac<0 then the curve does not cross the x-axis. However, you have entered into the realm of complex numbers and you will have 2 solution of form x_1Re+-x_2Im

For example:" "2+-3i

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