Question

The number of zeroes for the polynomial $y = p\left( x \right)$ from the given graph is:

1) 3
2) 1
3) 2
4) 0

Answer 1

Hint: As we know, the number of zeroes for a polynomial is determined by the number of the times the graph of the polynomial intersects the $x$- axis. From the given graph, find out the number of times the graph of $y = p\left( x \right)$ cuts the $x$- axis. The number of times the graph intersects, that many zeros the polynomial has.

Complete step by step solution:
Zeroes of the polynomial are the points on the $x$- axis that makes the polynomial equals to 0 as the value of $y$ on the $x$- axis is always 0.
Now, we will see how many times the graph intersects the $x$- axis.
In the given graph of the polynomial, it intersects the $x$- axis only once, that is at the origin.
Hence, the number of zeroes for the graph is 1.
From the given options, (B) is the correct option.

Note: Students make mistakes by not including origin as the intersection point. Origin is the point where both $x$- axis and $y$- axis meet. If the graph does not intersect the $x$- axis at all, then the polynomial does not have any zero.