If squared difference of the zeroes of x2+px+45 is equal to 144 then find the value of p.

Question : If squared difference of the zeroes of x²+px+45 is equal to 144 then find the value of p.

Doubt by Ananya 

Solution : 
(α-β)²=144 (Given)
x²+px+45

a=1
b=p
c=45

α+β=-b/a = -p/1 = -p
αβ=c/a = 45/1 = 45

Using the Identity 

(α-β)²=(α+β)²-4αβ
144=(-p)²-4(45)
144=p²-180
144+180=p²
p=√324
p=±18