Equations of the second degree 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 an independent term. It is very important to recognize the standardized forms that arise from a classification of equations of the second degree, 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.
Equations of the second degree are divided into: complete equations and incomplete equations of the second degree.
1. Complete equations of the second degree:
They are those that have a second-degree term (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 an equation of this type is the following:
2 × 2 - 4x - 3 = 0
Note that the coefficient of the square term is generally 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 that exist in complete quadratic equations. Yes, it is clear that the square term cannot fail otherwise, this would not be an equation of the second degree.
Well, there are two types of incomplete equations of the second degree: those that lack the linear term (that is, the term “in x”) and those that lack the independent term (that is, the one without x)
In the first case, the term containing the coefficient named "b" is missing, so the type form will remain as follows:
ax ^ 2 + c = 0
The incomplete quadratic equation, in the second case, the independent term is missing, 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
