Quadratic Minima!!!
Consider the equation where and are positive integers. The roots of the above equation lie in the interval .
What is the minimum value of ?
The answer is 16.
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1 solution
Since a,b,c are positive we can say that f(0) > 0 and f(1)>0. so, c>0 and a-b+c>0 thus the minimum value of c is 1 and that of b is a. for roots to exist, D is >= 0 so b^2 - 4ac>=0 a^2 >= 4a so a(min) = 4 therefore a= 4, b=4, c=1