Question 1

The number of zeroes of a polynomial is where its graph crosses the x-axis.

Step 1 — Understand zeroes

Let's look at the graphs. The zeroes are x-intercepts. These are points where $y = p(x) = 0$. We count how many times the graph touches or crosses the x-axis.

Step 2 — Analyze graph (i)

The graph is a horizontal line. It is above the x-axis. It does not cross the x-axis.

$\boxed{\text{Number of zeroes = 0}}$

Step 3 — Analyze graph (ii)

The graph is a curve. It crosses the x-axis at three points. These are distinct points.

$\boxed{\text{Number of zeroes = 3}}$

Step 4 — Analyze graph (iii)

The graph is a curve. It crosses the x-axis at one point. This is a single point.

$\boxed{\text{Number of zeroes = 1}}$

Step 5 — Analyze graph (iv)

The graph is a parabola. It crosses the x-axis at two points. These are distinct points.

$\boxed{\text{Number of zeroes = 2}}$

Step 6 — Analyze graph (v)

The graph is a curve. It crosses the x-axis at four points. These are distinct points.

$\boxed{\text{Number of zeroes = 4}}$

Step 7 — Analyze graph (vi)

The graph is a curve. It crosses the x-axis at three points. These are distinct points.

$\boxed{\text{Number of zeroes = 3}}$

Answer

(i) 0 (ii) 3 (iii) 1 (iv) 2 (v) 4 (vi) 3