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

1 Answer
Jun 17, 2016

Answer:

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#