Second Degree Equations


Second degree equations are of the form ax^2 + bx + c = 0; where a, b and c are real numbers (which are not zero); where x is called variable or unknown; a and b are called coefficients of the unknowns and c is called the independent term. It is very important to recognize the standardized forms that arise from a classification of quadratic equations, also called quadratic equations.

Once you recognize them, you will be clear about what method, strategy or route you must follow to solve them. After having partially worked on this point, you can see how to solve quadratic equations, but before solving them, it is important to identify them.

Second degree equations are divided into: complete equations and incomplete second degree equations.

1. Complete equations of the second degree:

They are those that have a term of the second degree (that is, a term “in X2”), a linear term (that is, “in x”) and an independent term, that is, a number without x. An example of such an equation is the following:

2×2 – 4x – 3 = 0

Note that the coefficient of the square term is usually called a, the linear term is called by, and the independent term is called c, so in this case:

a = 2, b = -4 and c = -3.

For this reason, the type form of these equations is represented by the following general expression:

ax^2+bx+c=0

2. Incomplete second degree equations:

For simplicity, a quadratic equation is not complete when it is missing one of the three terms mentioned above that exist in complete quadratic equations. Yes, it is clear that the square term cannot fail, otherwise this would not be a quadratic equation.

Well, there are two types of incomplete equations of the second degree: those that lack the linear term (that is, the “in x” term) and those that lack the independent term (that is, the one that does not have x )

In the first case, the term containing the coefficient called “b” is missing, so the type form will remain as follows:

ax^2 + c = 0

The incomplete quadratic equation, in the second case, lacks the independent term, that is, the one that contains the coefficient called “c”, so the form of the type will now remain as follows: ax^2 + bx = 0