Let x2−(m−3)x+m=0 ( m∈R ) be a quadratic equation. Find the value of m for which
(i) both the roots are smaller than 2.
(ii) both the roots are greater than 2.
(iii) one root is smaller than 2 and the other root is greater than 2.
(iv) exactly one root lies in the interval (1,2) .
(v) both the roots lie in the interval (1,2) .
(vi) one root is greater than 2 and the other root is smaller than 1.
(vii) atleast one root lie in the interval (1,2) .
(viii) atleast one root is greater than 2.