Quadratic Equations - An Introduction

Quadratic equations are the algebra topic taught to grade ten or eleven students. The word quadratic means, degree two in mathematics. Therefore any equation in degree two is called a quadratic equation. The form of standard quadratic equation is written as given below:

ax² + bx + c = 0

Where, "a", "b" and "c" are the real numbers and "a" can't be zero because in that case the quadratic term "ax²" becomes zero and the equation itself lose its identity and change to linear equation (degree one) which can be written as "bx + c = 0".

Some examples of quadratic equations are given below to make their identity more clear.

1. 3x² + 2x + 5 = 0

2. - x² + 3x - 9 = 0

3. x² + 1 = 0

4. - 9x² - 6x - 8 = 0

5. 4y² + 9 = 3y

Keep in mind that any letter can be used as a variable in the equations as I used "x" and "y" in the examples above.

In standard form these equations have three terms; first term in degree two called the quadratic term, second term in degree one called the linear term and third term is a constant number as shown in above examples.

Look at example # 3, there are only two terms in the equation. The term with degree one (linear term) is missing because the coefficient for this term is zero. This example can be written in standard form as shown below:

x² + 0x + 1 = 0

Now you have understood the way to write quadratic equations, the next step is to know about solving these equations. There are many ways to solve, such as solve by graphing, factor method, square root method, completing the square method and last but not least the formula method to solve quadratic equations.

To solve these equations using factoring method basic knowledge of factoring polynomials is required. You can read my articles about factoring polynomials for deeper knowledge about the topic.

To use formula to solve these equations, students should be very confident in radicals and they specially should have good knowledge of square roots. There is a special character used in formula called discriminate and is denoted by "D". The value of "D" is calculated by using the following formula:

D = b² - 4ac

Or in other words, linear coefficient "b" squared minus 4 times quadratic coefficient "a" times the constant term "c".

These equations if plotted on the graph, make a special cup shaped curve called parabola. There is a separate unit in grade eleven or twelve text books to study about parabolas.

There are many applications of these equations in higher algebra and to solve equations in higher degrees.

For more math resources and math worksheets my site can be visited or click for free 2nd grade math worksheets, for your kids in 2nd grade.

Introduction to CLEP College Mathematics Examination

In order to determine how skilled people are in mathematics at the undergraduate level, the College Board set up the College Mathematics exam. This is one of the institution's CLEP examinations that are credited by more than three thousand colleges in the United States, which makes it possible to do away with the required entry courses in colleges.

There are a number of topics into which the College Mathematics Exam has been divided in the following manner:

* 25% - Probability & statistics

* 20% - Functions & their graphs

* 20% - Real number systems

* 15% - Other geometry and algebra topics

* 10% - Logic

* 10% - Sets

In the Sets subsection, the topics covered include subsets; union & subsection; venn diagrams; as well as the cartesian product. In the logic subsection, the topics are conditional statements; truth tables; necessary & sufficient conditions; disjunctions, conjunctions, implications, & negations; inverse, converse, & contrapositive; as well as hypotheses, conclusions, & counterexamples.

In the subsection of real number systems, the topics dealt with include odd & even numbers; prime & composite numbers; rational & irrational numbers; factors & divisibility; open & closed intervals; as well as absolute value and order. The topics in the subsection of functions are domain & range; properties & graphs of functions; as well as the composition of functions & inverse functions. Under probability & statistics, the topics include counting problems; simple conditional probability; computing of probabilities of both simple & compound events; median, mean, mode, & range; as well as standard deviation. And in the subsection dealing with additional topics, there are logarithms & exponents; complex numbers; perimeter & area of plane figures; applications from geometry & algebra; parallel and perpendicular lines; pythagorean theorem; properties of circles, rectangles, & triangles; as well as algebraic equations & inequalities.

It requires a maximum of ninety minutes to complete the sixty multiple-choice questions. The score is scaled between 20 and 80, and it takes a minimum of 50 to qualify.

There are more than 1,000 locations worldwide from where the College Mathematics exam is taken, and you may register online at the College Board's website.

Quadratic Equations - An Introduction

Quadratic equations are the algebra topic taught to grade ten or eleven students. The word quadratic means, degree two in mathematics. Therefore any equation in degree two is called a quadratic equation. The form of standard quadratic equation is written as given below:

ax² + bx + c = 0

Where, "a", "b" and "c" are the real numbers and "a" can't be zero because in that case the quadratic term "ax²" becomes zero and the equation itself lose its identity and change to linear equation (degree one) which can be written as "bx + c = 0".

Some examples of quadratic equations are given below to make their identity more clear.

1. 3x² + 2x + 5 = 0

2. - x² + 3x - 9 = 0

3. x² + 1 = 0

4. - 9x² - 6x - 8 = 0

5. 4y² + 9 = 3y

Keep in mind that any letter can be used as a variable in the equations as I used "x" and "y" in the examples above.

In standard form these equations have three terms; first term in degree two called the quadratic term, second term in degree one called the linear term and third term is a constant number as shown in above examples.

Look at example # 3, there are only two terms in the equation. The term with degree one (linear term) is missing because the coefficient for this term is zero. This example can be written in standard form as shown below:

x² + 0x + 1 = 0

Now you have understood the way to write quadratic equations, the next step is to know about solving these equations. There are many ways to solve, such as solve by graphing, factor method, square root method, completing the square method and last but not least the formula method to solve quadratic equations.

To solve these equations using factoring method basic knowledge of factoring polynomials is required. You can read my articles about factoring polynomials for deeper knowledge about the topic.

To use formula to solve these equations, students should be very confident in radicals and they specially should have good knowledge of square roots. There is a special character used in formula called discriminate and is denoted by "D". The value of "D" is calculated by using the following formula:

D = b² - 4ac

Or in other words, linear coefficient "b" squared minus 4 times quadratic coefficient "a" times the constant term "c".

These equations if plotted on the graph, make a special cup shaped curve called parabola. There is a separate unit in grade eleven or twelve text books to study about parabolas.

There are many applications of these equations in higher algebra and to solve equations in higher degrees.