What is the value of p for which the difference between the roots of the equation x^2 + px + 8 = 0 is 2?

We have the equation x² + px + 8 = 0. Given that difference of roots of this equation is 2.

We know that difference of roots = √(b²-4ac) / a or (√D)/a
So here,
=> Difference of roots = √(b²-4ac) / a
=> 2 = √(p²-4*1*8) / 1
=> 2 = √(p²-32)

Squaring both the sides,

=> 4 = p²-32  
=> p² = 36
=> p = +/- 6

So, the values of p for which difference between the roots of equation x² + px + 8 = 0 is 2 are 6 and -6.