Processing math: 100%

Introduction to Quadratic Equation

We will discuss about the introduction to quadratic equation in details.


Let us start with the following problem:

Suppose, in a school students of class IX collect $ 10.50. Each of them contributing the number of cents, which is 5 more than the number of students in the class.

To express the above statement in mathematical language,

Let the number of students in class IX be x

Each students contributes (x + 5) Cents

Total amount collected from the student = x (x + 5) Cents

According to the problem, total collection is $ 10.50 or 1050 Cents



Now from the given question we get,

x(x + 5) = 1050

⟹ x2 + 5x = 1050

⟹ x2 + 5x - 1050 = 0

Therefore, the equation x2 + 5x - 1050 = 0 represents the above statement.

 

The equation x2 + 5x - 1050 = 0 is formed of only one variable (unknown quantity) x.

Here, the highest power of x is 2 (two).

This type of equation is called Quadratic Equation.


Definition of Quadratic Equation:

If the highest power of the variable of an equation in one variable is 2, then that equation is called a Quadratic Equation.

Some of the examples of quadratic equations:—

(i) x2 - 7x + 12 = 0            

(ii) 3x2 – 4x – 4 = 0

(iii) x2 = 16

(iv) (x + 3)(x - 3) + 5 = 0

(v) 3z - 8z = 2

To know the highest power of the variable in an equation, it becomes, sometimes, necessary to simplify the expression involved in the equation.

For example, the highest power of x in the equation x4 + 7x = 35 may appear to be one, but on simplification we get 5x2 - 12x + 140 = 0.

So, it is a quadratic equation

Again, 4(3x2 - 7x + 5) = 2(4x2 - 7x + 4) looks like a quadratic equation, but, it is really a linear equation.

Assuming, x2 = z the equation x4 - 3x2 + 7 = 0 reduces to z2 - 3z + 7 = 0, which is a quadratic equation.

Hence, the equations involving higher powers can be reduced to a quadratic equation by substitution.

Quadratic Equation

Introduction to Quadratic Equation

Formation of Quadratic Equation in One Variable

Solving Quadratic Equations

General Properties of Quadratic Equation

Methods of Solving Quadratic Equations

Roots of a Quadratic Equation

Examine the Roots of a Quadratic Equation

Problems on Quadratic Equations

Quadratic Equations by Factoring

Word Problems Using Quadratic Formula

Examples on Quadratic Equations 

Word Problems on Quadratic Equations by Factoring

Worksheet on Formation of Quadratic Equation in One Variable

Worksheet on Quadratic Formula

Worksheet on Nature of the Roots of a Quadratic Equation

Worksheet on Word Problems on Quadratic Equations by Factoring








9th Grade Math

From Introduction to Quadratic Equation to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Worksheet on Area, Perimeter and Volume | Square, Rectangle, Cube,Cubo

    Jul 25, 25 12:21 PM

    In this worksheet on area perimeter and volume you will get different types of questions on find the perimeter of a rectangle, find the perimeter of a square, find the area of a rectangle, find the ar…

    Read More

  2. Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox

    Jul 25, 25 03:15 AM

    Volume of a Cube and Cuboid
    We will practice the questions given in the worksheet on volume of a cube and cuboid. We know the volume of an object is the amount of space occupied by the object.1. Fill in the blanks:

    Read More

  3. Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume

    Jul 24, 25 03:46 PM

    Volume of Cuboid
    Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measur…

    Read More

  4. Volume of a Cube | How to Calculate the Volume of a Cube? | Examples

    Jul 23, 25 11:37 AM

    Volume of a Cube
    A cube is a solid box whose every surface is a square of same area. Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure i…

    Read More

  5. 5th Grade Volume | Units of Volume | Measurement of Volume|Cubic Units

    Jul 20, 25 10:22 AM

    Cubes in Cuboid
    Volume is the amount of space enclosed by an object or shape, how much 3-dimensional space (length, height, and width) it occupies. A flat shape like triangle, square and rectangle occupies surface on…

    Read More