QUESTION: Find the quadratic equation,which has difference of roots equal to 2 and the difference of the squares of roots equal to 5

Answer 1

(x-r1)(x-r2)=0
now given r1-r2=2
and r1^2-r2^2=5
from the last equation
(r1-r2)(r1+r2)=5
2(r1+r2)=5
r1+r2=2.5 but
r1-r2=2

adding equation..
2r1=4.5, so now you have r1, and you can compute r2.

r1=2.25
r2=0.25

check squares..
2.25^2-.25^2= yep, 5