QUADRATIC EQUATION - DEFINITION, SOLVING BY FACTORING AND BY QUADRATIC FORMULA

Please study
Math Equations before Quadratic Equation
if you have not already done so.

There, we gave introduction to equations and
explained various terms such as Open Sentence,
Equation, Solution or Root(s) of an Equation,
Domain of the variable and Kinds of Equations.

That knowledge is a prerequisite here.

Here, we deal with equations in which the highest
exponent of the varaible(s) present is two.

Quadratic Polynomial or Quadratic Expression :

ax² + bx + c where a ( ≠ 0 ), b, c are constants which can take real number values,is called a Quadratic Polynomial or Quadratic Expression in x.

Quadratic Equation :

If the Quadratic polynomial or Expression is
equated to zero, it is called a Quadratic Equation.

ax² + bx + c = 0 where a ( ≠ 0 ), b, c are constants which can take real number values, is called a Quadratic Equation.

Methods to Solve a Quadratic Equation :

There are two methods, in general,
to solve a 2nd Degree equation.

1. Solving by Factoring
2. The Method of Solution by Quadratic Formula.

Solving by Factoring

In the Solving by Factoring Method,
we factorize the quadratic polynomial,
to get two linear factors and equate the
product of the two linear factors to zero.

We know, if ab = 0, then either a = 0 or b = 0 or both.

Using this idea, we equate each of the two linear
factors to zero and then solve the two Linear Equations,
to get the two roots or solution of the 2nd degree equation.

We explained a five step method for factorization of
Quadratic Polynomials in FACTORING QUADRATICS.

We explained this five step method
through Solved Examples, there.

We also gave some more problems
as an exercise with answers to check
your understanding of the process.

Learning that method is a prerequisite here.

Please study them first, if you have not
already done so, and then come back here.
I will wait for you.

We will take up the Quadratic Expressions
and equate the Quadratic Polynomials to zero
to form the equations and solve them.
They are given at the following Links.

Set 1 of Solved Examples and Exercise

Set 2 of Solved Examples and Exercise

Set 3 of Solved Examples and Exercise

Set 4 of Solved Examples and Exercise

Set 5 of Solved Examples and Exercise