
The number of zeroes of a polynomial is determined by the number of points where its graph intersects the x-axis.
Step 1: Identify the zeroes by observing the points where the given graph touches or crosses the x-axis.
Step 2: Count the number of intersections.
Conclusion: If the graph does not intersect the x-axis, the polynomial has 0 zeroes.
If it intersects once, it has 1 zero. If it intersects twice, it has 2 zeroes.
To determine the number of zeroes of a polynomial based on its graph, we need to identify the points where the graph intersects the x-axis.
These intersections represent the roots or zeroes of the polynomial.
The graph indicates two points where it crosses the x-axis.
Therefore, the number of zeroes of this polynomial is 2.
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).
In the given figure, graph of polynomial \(p(x)\) is shown. Number of zeroes of \(p(x)\) is
