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 *x*^{2} − 3*x* + 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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