https://file.aiquickdraw.com/mathbot/file/1726944988709gr80mow7.jpg

I see that you've uploaded an image containing a mathematical problem, which includes multiple sums, algebraic equations, and conditions. To assist you effectively, let me break down the key parts of the image and solve the specific queries within it. Here’s what I observed:

- The image contains multiple summation and series expressions, including an equation involving sums of \( nC_i^t nC_j = 2^B \).
- There are complex expressions with variables like \( z_1, z_2, \beta_i \), and modular arithmetic is referenced.
- The main question seems to revolve around finding the value of \( |a_1 + a_2| \), with possible answer choices provided as options.

Let's focus on solving the specific problem where the final question asks: "Then \( |a_1 + a_2| \) = ?"

From this, I'll start by interpreting the key parts of the problem and provide a step-by-step solution. Could you confirm if you'd like me to focus on the specific problem mentioned at the end regarding \( |a_1 + a_2| \), or would you like me to address another part of the image?

Determine the value of |a1 + a2| given the quadratic equation f(x) = -yx^2 + 4x + 1 where f(x) = (ax + b)^2.

Explore the deep analysis of algebraic expressions, combinatorial counts, and modular arithmetic. This page discusses the resolution of complex equations, the calculation of binomial coefficients, and the derivation of results using the quadratic formula.

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