A little revision on Quadratic Equations in the Class 8 section.
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 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;
Solving Quadratic equations
There are two ways to solve the quadratic equations.
- 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
For a quadratic equation where ; expression is called discriminant and is generally denoted by . Thus, discriminant .
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.