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

Jun 17, 2016

See explanantion

#### Explanation:

Consider the standard form $y = a {x}^{2} + b x + c$

where $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

The discriminant is:${b}^{2} - 4 a c$

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

If ${b}^{2} - 4 a c > 0$ then the curve crosses the x-axis and there are two solutions to y=0

If ${b}^{2} - 4 a c < 0$ 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 ${x}_{1} R e \pm {x}_{2} I m$

For example:$\text{ } 2 \pm 3 i$