Quadratic Form

Quadratic Form:In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example,4x^2 + 2xy - 3y^2\,\! is a quadratic form in the variables x and y.Quadratic forms occupy central place in various branches of mathematics: number theory, linear algebra, group theory (orthogonal group), differential geometry.In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is

ax^2+bx+c=0,\,

where x represents a variable, and a, b, and c, constants, with a ≠ 0.Quadratic functions, in mathematics, is a polynomial function of the form

f(x)=ax^2+bx+c,\quad a \ne 0.

The graph of a quadratic function is a parabola whose major axis is parallel to the y-axis.

Binomial Theorem

Binomial Theorem:Let me explain Binomial Theorem.The binomial theorem explains the power of the binomial.Binomial coefficient is the resulting coefficient of the expression. By using binomial theorem we can raise the power. For example, (x+y) is a binomial.We will discuss Problems on Binomial Theorem in the future blogs.

Linear Programming

Linear Programming:Let us understand about Linear Programming.Linear Programming is the universal method of most favorable part of limited wherewithal such as labor, substance, engine, resources etc., to quite a few competing behavior such as goods, services, jobs, projects, etc, on the fundamentals of known criterion of optimality.Now let us see what we mean by linear programming constraints.The linear inequalities or equations on the variables of a linear programming problem are called constraints. The conditions x >- 0, y >- 0 are called non-negative restrictions.Lastly let us see one example problem of linear programming.Let us solve linear programming.Example problem:

Solve:

Minimize: 4a + 5b + 6c

Here we can see the method of solving linear programming.

a + b >= 11

a - b <= 5 c - a - b = 0 7a >= 35 - 12b

a >= 0 b >= 0 c >= 0

Solution:

Step1: We use the equation c-a-b=0 to put c=a+b (>= 0 as a >= 0 and b >= 0) and so the linear

Programming is reduced to minimize.

=4a + 5b + 6(a + b)

=4a + 5b + 6a +6b

= 10a + 11b

Subject to

a + b >= 11

a - b <= 5 7a + 12b >= 35

a >= 0 b >= 0

The minimum occurs at the intersection of a - b = 5 and a + b = 11

This is the first step in solving linear programming.

Step2: The second step in solving linear programming involves the following step

By using Elimination method we can get the value of a = 8 and b = 3

To find the C value (substitute a and b value in c= a + b ) c = 11

The value of the objective function 10a + 11b = 80 + 33 = 113.

Thus these are the steps involved in solving linear programming.

Least Common Multiple

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Least Common Multiple: In arithmetic number of theory is the least common multiple or lowest common multiple (LCM) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple of both of a and of b. Since it was a multiple, it can be divided by a and b without a reminder.If either a or b is 0, so that number is no such positive integer, then LCM(a, b) is defined to be zero.Now let us find least common multiple,Multiples of 4 are:4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, ......................Multiple of 7 are:7, 14, 21, ................These were some examples of least common multiple lcm.ope you like the above example of Least common Multiple.Please leave your comments, if you have any doubts.

Probability

What is probability:Let us now understand what is a Probability.An experiment repeated under essentially homogeneous and similar conditions results in an outcome, which is unique or not unique but may be one of the several possible outcomes. When the result is unique then the experiment is called a probability.Usually questions are asked on how to calculate probability.In the future blogs we will learn about probability calculator.

Matrices Determinants

Matrices Determinants:Let us learn matrices determinants.Matrices :A rectangular array of entries is called a Matrix. The entries may be real, complex or functions. The entries are also called as the elements of the matrix. The rectangular array of entries are enclosed in an ordinary bracket or in square bracket.Determinants : Let A = [aij] be a square matrix. We can associate with the square matrix A, a determinant which is formed by exactly the same array of elements of the matrix A. A determinant formed by the same array of elements of the square matrix A is called the determinant of the square matrix A and is denoted by the symbol det.A or |A|.The above explanation speaks about deteminants and matrices,in the coming Blogs we will learn about determinants of matrices.

Binomial Theorem

Let us learn about Binomial Theorem in this Blog.The binomial theorem explains the power of the binomial. Binomial coefficient is the resulting coefficient of the expression. By using binomial theorem we can raise the power. For example, (x+y) is a binomial. Binomial Distribution is a statistical experiment which means the number of successes in n repeated trials of a binomial experiment. It is also called as Bernoulli distribution or Bernoulli trial.For example:For a clinical trial, a patient may live or die. Here the researcher faces the number of survivors and not how much time the patient lives after treatment.H