Question

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

Answer 1

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`