The graph of $y=p(x)$ is given below for a polynomial $p(x)$. Find the number of zeroes of $p(x)$.
(N/A) The number of zeroes of a polynomial $p(x)$ is equal to the number of points where the graph of $y=p(x)$ intersects the $x$-axis.
In the given graph,the curve intersects the $x$-axis at $3$ distinct points.
Therefore,the number of zeroes of the polynomial $p(x)$ is $3$.
In the given graph,the curve intersects the $x$-axis at $3$ distinct points.
Therefore,the number of zeroes of the polynomial $p(x)$ is $3$.
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Part $I$ Part $II$ $1.$ The graph of $p(x)=x^{2}-5x+6$ $a.$ Intersects the $X$-axis at one point. $2.$ The graph of $p(x)=x^{2}-10x+25$ $b.$ Intersects the $X$-axis at zero points. $3.$ The graph of $p(x)=x^{3}-4x$ $c.$ Intersects the $X$-axis at two points. $4.$ The graph of $p(x)=x^{2}+4x+5$ $d.$ Intersects the $X$-axis at three points.
| Part $I$ | Part $II$ |
| $1.$ The graph of $p(x)=x^{2}-5x+6$ | $a.$ Intersects the $X$-axis at one point. |
| $2.$ The graph of $p(x)=x^{2}-10x+25$ | $b.$ Intersects the $X$-axis at zero points. |
| $3.$ The graph of $p(x)=x^{3}-4x$ | $c.$ Intersects the $X$-axis at two points. |
| $4.$ The graph of $p(x)=x^{2}+4x+5$ | $d.$ Intersects the $X$-axis at three points. |
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