Given quadratic equation is: x2−mx+4=0 Both the roots are real and distinct. So, discriminant B2−4AC>0 ∴m2−4⋅1⋅4>0 ∴(m−4)(m+4)>0 ∴m∈(−∞,−4)∪(4,∞) ........(i) Since, both roots lies in [1,5] ∴−
−m
2
∈(1,5) ⇒m∈(2,10) And 1⋅(1−m+4)>0⇒m<5 ∴m∈(−∞,5)... (iii) And 1⋅(25−5m+4)>0⇒m<
29
5
∴m∈(−∞
29
5
)...(iv) From (i), (ii), (iii) and (iv), m∈(4,5)