Question

plzzzzzzzzzz give me the class 10 notes chapter no. 2​

Answer 1

Here r ur notes:

Polynomial:

A polynomial is defined as an expression of two or more algebraic terms. The term polynomial itself means “poly” (means many) and “nomial” (means terms). A polynomial can consist of constants, variables, and even exponents. Check out this detailed polynomials article to understand about this topic it in detail and to get further information.

Standard Form of a Polynomial:

[a0 xn + a1 xn – 1 + a2 xn – 2 + …….. + an x2 + an – 1 x + a­n]

Degree of a Polynomial:

In a polynomial, the highest power of the polynomial is referred to as the degree of the polynomial.

Types of Polynomials

There are three main types of polynomials which are linear, quadratic, and cubic polynomial according to the degree of that polynomial.

Degree Type of Polynomial

1 Linear Polynomial

2 Quadratic Polynomial

3 Cubic Polynomial

The above table can be explained as “a polynomial with degree 1 is known as a linear polynomial, a polynomial with degree 2 is binomial or quadratic polynomial, whereas with degree three is cubic polynomial.”

Root or Zeroes of a Polynomial

For any given polynomial, the value of x obtained by substituting the value of polynomial as 0 is known as the zero of the polynomial. These are also termed as roots of the equation.The Graphical meaning of the zeros of the polynomial is that the curve cuts the x-axis a point (k,0), where k is the root of the polynomial.

Notes: A polynomial of degree n will have n roots. So, any quadratic polynomial can only have a maximum of 2 zeroes and any cubic polynomial will have 3 zeroes maximum.

A quadratic equation ax2 + bx + c = 0 will have 2 roots, say α and β.

The sum of roots (α + β = -b⁄a)

Product of the roots (αβ = c⁄a)

Division Algorithm

According to division algorithm, any polynomial p(x) and any non-zero polynomial g(x), there exists polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).

Probability:

The probability of an event can be defined as the likelihood of an event to occur. There are mainly two types of probability which are experimental probability and theoretical probability.

Experimental Probability

Experimental probability or empirical probability can be defined as the probabilities of events in which the results of actual experiments are considered. The formula for empirical probability is-

P(E)=NumberoftrialsinwhichtheeventhappenedTotalnumberoftrials

Theoretical Probability

Theoretical probability is defined as the probability which is based on reasoning and expectations. The formula for theoretical probability is given as-

P(E)=NumberoftrialsinwhichtheeventhappenedThetotalnumberoftrials

Events and its types

An event can be defined as a possible outcome of an experiment. There are various types of events in probability which are explained in the linked article. The events are extremely important and should be thoroughly understood.

Important Terms in Probability

The probability of a Sure Event 1

The probability of an Impossible Event 0

Probability Range 0 to 1

Sample Space It is defined as the superset of all possible outcomes in an experiment.

Elementary Event It is an event which has only 1 outcome

Complementary Events The complement of an event “X” is the event that is “not X”. It is represented as P(X’). Also, P(X) + P(X’) = 1

Hope it helps!!

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