Find the set of possible values of 'm' for which x^2 - (m^2 - 5m + 5)x + (2m^2 - 3m - 4) = 0 has roots whose sum and product are both less than 1.

We have the equation x^2 - (m^2 - 5m + 5)x + (2m^2 - 3m - 4) = 0;

Sum of roots = (m^2 - 5m + 5)
Product of roots = (2m^2 - 3m - 4)

Given that both the sum and product of roots are < 1.

So,

m^2 - 5m + 5 < 1
=> m^2 - 5m + 4 < 0
=> m^2 - m - 4m + 4 < 0
=> m(m - 1) - 4(m - 1) < 0
=> (m - 4)(m - 1) < 0

To satisfy this, m should lie in (1, 4)

Also,

2m^2 - 3m - 4 < 1
=> 2m^2 - 3m - 5 < 0
=> 2m^2 + 2m - 5m - 5 < 0
=> 2m(m + 1) - 5(m + 1) < 0
=> (m + 1)(2m - 5) < 0

To satisfy this, m should lie in (-1, 5/2)

To satisfy both, our answer should be the intersection of (1, 4) and (-1, 5/2) which comes out to be (1, 5/2)