POLYNOMIALS

Important definitions

Variable: It changes its values according to the condition given.

As Ram's Age is not known, assume (x) years.

Example-

Rohit's income is not given, so assume x in rupees.

Here, we can see that we have assumed the value x in two different categories

Constant

It does not change

As -2, 5, 7, 1000, etc.

Types of polynomials

Monomial: An expression containing a single term

ex - ax^2
Binomial: An expression containing two variables

Example : x +y, x^2 +y^2

Trinomial

An expression containing three variables is called a trinomial - x +y +z

* An expression containing more than three variables is said to be a polynomial

We express a polynomial by writing the symbol p(x)

The value of a variable that makes the polynomial zero is said zero of the polynomial.

Alternatively, we obtain zero when we substitute the variable's value into the expression, and it yields the answer zero.

Example: Find the zero of the polynomial

p(x): x^2 -4

"^" is used to show the power

If you put x=2 in the p(x), see what you get-

p(2): 2^2 -2 = 4-4 =0

So, X=2 is the zero of the polynomial p(x).

Very simple, in the graph, see how many times the curve or the line crosses or touches the X-axis, which will give you the number of zeros.

(Question figure given in the textbook)

(i) In the first graph, you can see line is parallel to the X axis; it does not touch or cut the X axis. So, the number of zeros = 0

(ii) The curve crosses the X-axis one time; therefore, the number of zeros = 1.

(iii) The curve crosses the X axis for three times; hence, the number of zeros is =3

(iv) It is easily seen that the curve crosses the X axis, so the number of zeros = 2.

(v) The curve crosses the x-axis four times. Hence, the number of zeros = 4

(vi) The curve crosses the X axis once and touches it once, hence, the total solution = 2

----End of Chapter 2.1 -----

The next chapter, 2.2, will be available shortly on the other page.

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