Answer:
(5/4)√17
Step-by-step explanation:
You can use the roots given by the quadratic formula and find the difference of their squares.
x1 = (-b +√( ))/(2a) . . . . . one of the two roots
x2 = (-b -√( ))/(2a) . . . . . the other root
We'll use the fact that a^2-b^2 = (a+b)(a-b) to find the difference of the squares of the roots.
x1+x2 = -b/a
x1-x2 = √( )/a
And the product of these is ...
x1^2 -x2^2 = (x1+x2)(x1-x2) = -b√(b^2 -4ac)/a^2
For the given quadratic, this difference is ...
= -(-5)/(2^2)·√((-5)^2 -4(2)(1)) = (5/4)√17
