Assuming you know the quadratic formula:
[tex]x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
You can fill in a, b and c in this and get:
[tex]x = \frac{4 \pm \sqrt{16-8p}}{4}[/tex]
Now, let's create a shorthand [tex]q = \frac{\sqrt{16-8p}}{4}[/tex] to make the writing easier:
[tex]x = 1 \pm q[/tex]
But since one root is three times the other root (but we don't know which one), we also know that:
[tex]1 + q = 3(1-q)[/tex] or [tex]1 - q = 3(1+q)[/tex]
If you solve this, you get:
[tex]q = \frac{1}{2}[/tex] or [tex]q = -\frac{1}{2}[/tex]
However, since q is a square root, it must be postive.
So we know that:
[tex]\frac{\sqrt{16-8p}}{4} = \frac{1}{2}[/tex]
From this you find that
[tex] 16-8p = 4 [/tex]
So p = 3/2
The roots are x=1/2 and x=3/2.
