Question

find the value of a such that function f given by f(x) equal to x^2 + ax + 1 is strictly increasing on (1,2)

Answer 1

Since, coefficient of x^2 is positive therefore the graph will have opening upward. So, if we compare and see general form of quadratic equation we can get that a quadratic function strictly increases is it has opening upwards for x>= (-b/2a) where a and b are the coefficient of x^2 and x in general quadratic equations.
Now , coming to your question
it will strictly increases if 1>(-a/2)
Therefore on solving inequality we get
a<-2 and there is also a condition given that for x€ (1,2) therefore
a>-4

so, a€(-4,-2)