Question

The polynomial x^3-ax^2+bx-2010 has three positive integer zeros. What is the smallest possible value of A?

Answer 1

I guess we will have to use results of sum of roots and product of roots for an equation of degree 3.

Answer 2

i would use calculus, 1st and 2nd derivative to find the smallest value of a...

Answer 3

@mathsmind The method of using derivatives is to find the value of x at which the function is minimum right?

Answer 4

yes

Answer 5

when it says what is the smallest possible value it is the same as what we understand in optimization, or max/min concepts

Answer 6

@mathsmind 1st derivative condition gives the stationery points and 2nd derivative will tell if its the maximum or minimum point. Here the 1st derivative has terms involving x,a and b. I am stuck. Could you please elaborate a bit more?

Answer 7

if the 2nd derivative is > 0, and we know that a,b, and c are +ve integers then we should get the smallest possible value for a, there is another way to solve this problem by using the concept of vertex...