a quadratic equation for two unknown number find values of $p$ such that the equation $4x^2 + 3px - 2p = 0$ has? below are a few choices of the value p:
a) 2 real roots
b) 1 real roots
c) no roots or complex roots

so far i did for a) 2 real roots
$$(3p)^2 - 4(4)(-2p) > 0\\
9p^2 +32p > 0\\
9\left( p^2+\frac{32p}{9} \right) > 0\\
p^2+\frac{32p}{9} > 0\\
p^2 +\frac{32p}{9} + \left(\frac{32}{18}\right)^2 > 0\\
\left(p + \frac{32}{18} \right) ^2 > 0 \\
p + \frac{32}{18} > 0\\
p > -\frac{32}{18} $$

The roots are given by the quadratic formula:
$$
r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\
= \frac{-3C \pm \sqrt{9C^2 + 32p}}{2a} 
$$
If the thing under the square root is positive, you'll get two roots. Under what conditions will you get just one? Under what condition will you get none? 
