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Polynomials

A polynomial in variable x is denoted by p(x).

The highest power of the variable in the polynomial is known as its degree. For example, the highest power of variable x in the polynomial x2 − 3x + 2 is 2. Hence, it’s degree is 2.

Let us understand the concept of zeroes of a polynomial with the help of the given video.

Let us better understand this concept with a few more examples.

Example1:

Find the number of zeroes of the polynomial whose graph is given below.

Solution:

The given graph intersects the x- axis at 4 distinct points.

Hence, the number of zeroes of the given polynomial is 4.

Example 2:

Find the number of zeroes of the polynomial whose graph is given below.

Solution:

The given graph does not intersect the x-axis.

Hence, the given polynomial has no zeroes or in other words, the number of zeroes of the given polynomial is zero.

Example 3:

Find the number of zeroes of the polynomials whose graphs are given below.

                      (a)                                          (b)                                      (c)

 

                    (d)                                           (e)                                           (f)

                (g)                                               (h)                                        (i)

                 (j)                                              (k)                                          (l)

Solution:

(a) The graph intersects the x-axis at only 1 point.

Hence, the number of zeroes of this polynomial is 1.

(b) The graph intersects the x-axis at 4 distinct points.

Hence, the number of zeroes of this polynomial is 4.

(c) The graph intersects the x-axis at only 1 point.

Hence, the number of zeroes of this polynomial is 1.

(d) The graph of the polynomial does not intersect the x-axis.

Hence, this polynomial has no zeroes.

(e) The graph intersects the x-axis at 2 distinct points.

Hence, the number of zeroes of this polynomial is 2.

(f) The graph intersects the x-axis at 2 distinct points.

Hence, the number of zeroes of this polynomial is 2.

(g) The graph of the polynomial does not intersect the x-axis.

Hence, this polynomial has no zeroes.

(h) The graph intersects the x-axis ...

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