In elementary algebra, a quadratic equation is any equation having the form

where represents an unknown, and represent known numbers such that .

If , then the equation is linear, not quadratic.

The numbers are the coefficients of the equation, and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.

The degree of a quadratic equation is 2.

Examples of quadratic equations:

Roots of Quadratic equations

Every quadratic equation is satisfied by two values say . These values, , are said to be the root of the equation.

What this also means is that

Note: Zero Product Rule: Whenever the product of the two expression is zero, then at least one of those is zero. In the above example;

or

Solving Quadratic equations

There are two ways to solve the quadratic equations.

Factorization Method

Step 1: Factorize

Step 2: Equate each linear part to zero.

Step 3: Hence

Using the Formula

Step 1: From the quadratic equation, first identify .

Then use the following formula

Discriminant:

For a quadratic equation where ; expression is called discriminant and is generally denoted by . Thus, discriminant .

Nature of the roots of the equations:

If represent real numbers and , then discriminant:

the roots are real and equal.

the roots are real and unequal.

the roots are imaginary.

Square root of a negative number like is an imaginary number.

Therefore, just be looking at , we can tell the nature of the roots.

Note: Problems based on Geometrical Figures: The problems where you have a right triangle (where Pythagoras theorem is used) would see the application of the quadratic equation.