# Do the root shuffle

**Algebra**Level 5

\(f(x)\) and \(g(x) \) are monic quadratic polynomials that satisfy the following conditions:

- \(f(x) = 0 \) has real distinct roots \( a_1 \) and \(a_2\).
- \(g(x)= 0 \) has real distinct roots \( b_1\) and \( b_2\).
- \( \{ f(b_1), f( b_2) \} = \{ b_1, b_2 \} \).
- \( \{ g( a_1), g(a_2) \} = \{ a_1, a_2 \} \).
- \(f(1)g(1) = 132 \).

What is the value of \(f(2)g(2)?\)

**Details and assumptions**

A polynomial is **monic** if its leading coefficient is 1. For example, the polynomial \( x^3 + 3x - 5 \) is monic but the polynomial \( -x^4 + 2x^3 - 6 \) is not.