Vieta's Derivative II -- My 500-follower problem

Calculus Level 4

The function \(x^5 + 6x^4 - 18x^3 -10x^2 + 45x -24\) has only four distinct real roots: \(\alpha\), \(\beta\), \(\gamma\) and \(\delta\) (in no particular order). If \(f'(x)\) is the first derivative of \(f(x)\). Evaluate

\[f'(\alpha) + f'(\beta) + f'(\gamma) + f'(\delta) \]

Inspiration: This is exactly the problem titled Inspired by Vieta's Derivatives with a twist.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.