If the difference between the roots of the equation x^2 + px + 8 = 0 is 2 then what is the possible value if P?

Question

Let a1 and a2 be the roots or the equation (x- a)(x - b) = c and c != 0, then what are the roots of the equation (x - a1)(x - a2) + c = 0?

Answer 1

Roots of the equation will be
(-p+(p^2-32)^0.5)/2 & (-p-(p^2-32)^0.5)/2
difference between the roots
= - (p/2) + (p/2) + ((p^2-32)^0.5)/2) + ((p^2-32)^0.5)/2) = 2
= ((p^2-32)^0.5) = 2
= p^2 -32 = 4
=> p = 6

So to cross-check the roots of the equation x^2 + 6x + 8 = 0 are x = -2 & -4. & since -2 - (-4) = 2, p=6 holds good.