# Maximum and Minimum Roots

Algebra Level 5

Consider all polynomials $$P_c (x) = x^3 - 2x^2 - 4x + c$$ which have 3 real roots. The difference between the maximum possible root of such a polynomial, and the minimum possible roots of such a polynomial, can be expressed as $$\frac{a}{b}$$ for positive coprime integers. Find $$a + b$$.

Note: The value of $$c$$ need not be identical in the maximum and minimum cases.

×

Problem Loading...

Note Loading...

Set Loading...