# Funny Polynomial!

Algebra Level 4

$P(x) = 24x^{24} +\displaystyle \sum_{j = 1}^{23}(24 - j)(x^{24 - j} + x^{24 + j}).$ Let $$z_{1},z_{2},\ldots,z_{r}$$ be the distinct zeros of $$P(x)$$ and let $$z_{k}^{2} = a_{k} + b_{k}i$$ for real $$a_k ,b_k$$, $$k = 1,2,\ldots,r,$$ Let

$$\displaystyle\sum_{k = 1}^{r}|b_{k}| = m + n\sqrt {p},$$ where $$m,n,$$ and $$p$$ are integers and $$p$$ is not divisible by the square of any prime. Find $$m + n + p.$$

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