Polynomials - NCERT Class 10 Maths

Question 1

The graphs of \(y{ }={ }p\left( x \right)\) are given in the figure below, for some polynomials \(p\left( x \right)\). Find the number of zeroes of \(p\left( x \right)\) in each case.

Solution

Video Solution

What is known?

The graphs of \(y{ }={ }p\left( x \right)\) are given in the above figure for some polynomials \(p\left( x \right)\).

What is unknown?

The number of zeroes of \(p\left( x \right)\) in each case.

Reasoning:

You can reach the solution easily by understanding the statement of the question. As The graphs of \(y{ }={ }p\left( x \right)\) are given and you have to find the number of zeroes of \(p\left( x \right)\) in each case.

To find this look at the graphs and visually find how many points it cuts the \(x\)-axis. The number of points the graph cuts or touches the \(x\)-axis. The number of points it cut or touches the \(x\)-axis are the zeroes of the polynomial \(p\left( x \right)\).

Steps:

(i) The number of zeroes is \(0\) as the graph doesn’t cuts the \(x\)-axis at any point.

(ii) The number of zeroes is \(1\) as the graph cuts the \(x\)-axis at only one point.

(iii) The number of zeroes is \(3\) as the graph cuts the \(x\)-axis at \(3\) points.

(iv) The number of zeroes is \(2\) as the graph cuts the \(x\)-axis at \(2\) points.

(v) The number of zeroes is \(4\) as the graph cuts the \(x\)-axis at \(4\) points.

(vi) The number of zeroes is \(3\) as the graph cuts the \(x\)-axis at  \(3 \) points.