ISI 2013 sample paper

[Nag27]

Hi,

With regards to Question 9 in ME I section of the latest sample paper -- How does the roots of a third degree polynomial change with the introduction of absolute value signs?

Thanks

[Amit Goyal]

You don't need to find the roots. It is obvious that
|x|^3 + a|x|^2 + b|x| + c = 0 has no solution for positive values of a, b and c. Hence the minimum roots possible is 0.

[Nag27]

Thanks Amit! Is Sturm's Theorem useful for solving such questions (when they don't have a straightforward solution) ? Can you suggest a book or problem set for such questions?