quadratic equations in algebra

In the previous post we have discussed about how to calculate the domain of a function
 and In today's session we are going to discuss about quadratic equations in algebra. By algebra quadratic equations, we mean that equation written in the form of ax² + bx + c = 0, where we have a ≠ 0.
We say that in above equation, if a = 0, then degree of above equation will become 1, so we say that above equation will be converted in the form of linear equation. As the degree of these equations is 2, so it has two zeroes. It indicates that any quadratic equation has two roots which are represented as (alpha) or (beta). Moreover these roots can be real or imaginary.
There are different ways to find the roots of the quadratic equations. One of the common method to find the roots of the quadratic equation is by finding the factors. These factors can be calculated by splitting the middle term or even by finding the value of the 'x', where the equation becomes zero. Thus we say that we find the zeroes of the given quadratic equations. In some cases, we say that the quadratic equation roots can also be calculated by finding the D = b² – 4 * a * c.
 Now we come to the following three conclusions after getting the value of D:
1.    If the value of D = 0, then the roots are real and equal.
2.    If D< 0, then the roots are imaginary.
3.    If D > 0, then the roots are real and unequal.
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how to calculate the domain of a function

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Function is a tool that is used to verify the relationship among given values. Now we will understand the concept how to find the domain of a function. Before finding the domain of any function and relation first of all we will learn about the domain of a function.

Set of inputs for a function is called as domain of function. Similarly we can say that set of all possible outputs corresponding to inputs is as known range of function. This concept can be understood with help of an example:

For example: Suppose we have some values (16, -51), (-19, 41), (110, -91), (-105, 198), find the domain of the given elements?

Solution: According to the definition of domain of function we can choose the domain values of above function.

Domain of a given function = 16, -91, 110, -105. Range of a function is given as:

Range is all ‘y’ coordinate values,

Range = - 51, 41, -91, 198.

Domain can be found using steps shown below:

Step 1: To calculate value first take a function or a relation which has ‘x’ and ‘y’ values.

Step 2: As we see above domain of function or relation is all input values.

This is how we can find the domain and range value of a given function and relation.

Multiplying Rational Expressions gives us a simplest form of any rational expression.

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