Elimination method:

A ordered pair (x₁,y₁) s called a solution to a linear system in two variables if the values x = x₁ and y = y₁ satisfy all the equations in the system. This page will contain 10 questions to solve equations by using elimination method.

Examples of elimination method

Elimination method worksheet

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Cross multiplication method:

To write the given equation in the form of a/b = c/d and solving for the given variables is called cross multiplication method. This page will contain some set of question for practice. For each questions you can get solution.

Examples of cross multiplication method

Cross multiplication method worksheet

Quadratic equation from roots:

General form of quadratic equation with roots α and β is

x² - (α + β) x + αβ = 0.

• α + β = Sum of roots
• α β = Product of roots

Examples of quadratic equation from roots

Quadratic equation from roots worksheet

Synthetic division:

Synthetic division is a short cut method of polynomial division. The condition to be used this method is, the divisor must of be of first degree and should be in the form (x-a)

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Examples of synthetic division

Synthetic equation worksheet

Practice problems of factoring cubic equation

Factoring quadratic equation:

An equation which is in the form of ax² + b x + c =0,where a,b,c ∈ R and a≠0 is called a quadratic equation. Splitting the given equation into two linear equations known as (x + a) (x + b) is  called factoring the quadratic equation.

Examples of factoring

Factoring quadratic equation worksheet

More problems in factoring equation

GCD:

GCF -Greatest common factor is the largest common factor of two or more numbers.

Examples of GCD

GCD worksheet

L.C.M

LCM of two or more non zero whole numbers is the smallest whole number which is a multiple of each given number. In other words it must be the smallest whole number which is divisible by each number.

Examples of L.C.M

L.C.M worksheet

Word problems of L.C.M & G.C.D

Combined worksheet of L.C.M & G.C.D

Relationship between zeroes and coefficients:

Consider the equation ax² + bx + c = 0. where a,b and c ∈ R.  We can solve this quadratic equation by using quadratic formula. Then we get α and β as two roots of the equation. Now we are going to see the concept how to find sum of roots α + β and product of roots α β.

Examples of relationship between zeroes and coefficients

Relationship between zeroes and coefficients worksheet

Simplifying Rational expression:

Two rational expressions can be simplified using factorization. This process is known as simplifying rational expression.

Example of simplifying rational expression

Worksheet of simplifying rational expression

Practical use of quadratic equations:

In this page you can find some set of questions to show the practical use of quadratic equations.

Example problems

Worksheet of practical problems

Nature of roots:

The roots of the quadratic equation ax² + bx+ c = 0 are [- b ± √(b² - 4 ac)]/2a. The nature of roots depends on the value b² - 4 ac. The value of the expression b² - 4 ac discriminates the nature and so it is called the discriminant of the quadratic equation. It is denoted by symbol ∆.

Example of nature of roots

Worksheet nature of roots

Framing quadratic equation from roots:

General form of quadratic equation with roots α and β is

x² - (α + β) x + αβ = 0.

• α + β = Sum of roots
• α β = Product of roots

Example of quadratic equation from roots

Worksheet of framing quadratic equation from roots