Correct answer: 4
Explanation:
A biquadratic polynomial is a polynomial of degree 4.
According to the Fundamental Theorem of Algebra, a polynomial of degree n can have at most n real or complex zeroes.
Therefore, a biquadratic polynomial can have at most 4 zeroes.
Let \( M \) be a \( 7 \times 7 \) matrix with entries in \( \mathbb{R} \) and having the characteristic polynomial \[ c_M(x) = (x - 1)^\alpha (x - 2)^\beta (x - 3)^2, \] where \( \alpha>\beta \). Let \( {rank}(M - I_7) = {rank}(M - 2I_7) = {rank}(M - 3I_7) = 5 \), where \( I_7 \) is the \( 7 \times 7 \) identity matrix.
If \( m_M(x) \) is the minimal polynomial of \( M \), then \( m_M(5) \) is equal to __________ (in integer).