2026/046) Find the sum of the real roots of the polynomial $\prod_{k=1}^{100} (x^2-11x +k)$

 It is product of 100 terms. 

From each term we shall have 2 solutions. 

Either both the solutions are real or complex

Let check which and how many terms shall have real roots

$x^2 - 11x +k$ has real root if discriminant is positive or zero 

That is $11^2 - 4 * k \ge 0$ or $ k \le 30$

There are 30 terms for which it has got real roots and sum of real roots in each term is 30 giving sum of real roots 330