Defination of a quadratic equation

Quadratic Polynomial :

A polynomial of the second degree is called a quadratic polynomial. The general form of a quadratic polynomial is ax^2+bx+c; where a,b and c are real numbers, a not equal to 0 and x is a variable.

Example :

x^2 – 6x +4

Quadratic Equation:

An equation p(x) = 0, where p(x) is a quadratic polynomial, is called a quadratic equation. The general form of a quadratic equation is ax^2+bx+c where a, b and c are real numbers, a not equal to 0 and x is a variable.

Example:

x^2-2x+2 = 0

Function

A function is a rule which associates two or more than two variables. Functions can be understood with the help of a very simple basic example :

1. IF the distance (d) is constant, then the time taken (t) to cover that distance (d) will be dependent on the value of the speed (v). This can be written mathematically as t = f(v)

Normally any function is represented in the format of y = f(x)

Process to find out HCF

How to find out the HCF (Greatest Common Divisor) -

Step1 : Factories all the numbers into their prime factors.

Step2 : Collect all the common factors.

Step3 : Raise each factor to its minimun available power and multiply.

Example Find HCF of 100, 200 and 250

Step1 :

100 = 2^2 * 5^2

200 = 2^3 * 5^2

250 = 5^3 * 2^1

Step2 :

2 , 5

Step3 :

2^1 * 5^2 = 50

Process to find LCM

How to find the LCM (Least common multiple) -

Step1 : Factorize all the numbers into their prime factor.

Step2 : Collect all the distinct factors.

Step3 : Raise each factor to its maximum available power and multiply.

Example Find LCM of 10,20,25

Step1 :

10 = 2^1 * 5^1

20 = 2^2 * 5^1

25 = 5^2

Step2 :

2,5

Step3:

2^2 * 5^2 = 100

The biggest advantage of using this method lies in the fact that we can find out the LCM of any number of numbers in a straight line without using the conventional method.

Formula is No Formula :)

Yesterday i was having a chatting with my cousin about Probability. Why people find it tough and hard to solve the problems, even i am of one them. He gave me a simple answer….

No Formula.

Try to solve the problem using your Common Sense instead of looking for the formula. Then we discussed couple of problem and i really find it easy to solve the problem with him.

So here is the formula to solve the probability problems – No Formula

Questions? Answers :)

questions H.C.F

Q1 -  Find the greatest number that will divide 185 and 300 leaving remainder 3 and 5 respectively.

A1 – Since dividing 185 the remainder left is 32, 182 will be exactly divisible by that number.

Similarly 300-6 = 294 will be exactly divisible by the number.

So the required H.C.F  of 182 and 294 is 2 * 7 = 14

Q2 – Find the H.C.F of (2x^2 – x -1) and (4x^2 + 8x + 3)

Try this one…..

Ans is ( 2x + 1)

Linear Equations in One Variable

An equation is an equality connecting some unknowns. The unknowns are represented by “letters” and are called “the variables”. If the equation has only one unknown, it is called “an equal in one variable”. The word “Linear” means “of degree one”. Hence if only a single variable with degree one occurs in an equation, it is called a linear equation in one variable.

 An equation of one variable and of first order (i.e., its highest power is one) is called a Linear equation. Such an equation has only one solution. A solution is also called the ‘root’ of the given equation. 

Question : Solve  ?

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