Algebra basics terms
A Quadratic Equation is an equation of the second degree, containing but one unknown quantity.
A Pure Quadratic Equation is a quadratic equation involving only the square of the unknown quantity; as, 2 a^ = 5.
An Affected Quadratic Equation is a quadratic equation involving both the square and the first power of the unknown quantity
A pure quadratic equation may be solved by reducing it, if necessary, to the form x^ = a, and then extracting the square root of both members.
A trinomial is a perfect square when its first and third terms are perfect squares and positive, and the second term plus or minus twice the product of their square roots
The square root of the third term is equal to the second term divided by twice the square root of the first.
An equation is said to be in the quadratic form when it is in the form
F(x) = ax2
F(x,y) = ax2 + by2 + cxy
F(x,y,z) = ax2 + by2 + cz2 + dxy + exz + fyz
Two equations of the second degree with two unknown quantities will generally produce, by elimination, an equation of the fourth degree with one unknown quantity ; the rules already given are, therefore, not sufficient for the solution of all cases of simultaneous equations of the second degree with two unknown quantities.
It has already been shown that a single equation containing two or more unknown quantities is satisfied by an indefinitely great number of sets of values of these quantities; and, in general, that a set of m independent equations containing more than m unknown quantities is satisfied by an indefinitely great number of sets of values of the unknown quantities involved in it. Such equations are called indeterminate. If, however, the unknown quantities are required to satisfy other conditions, the number of solutions may be finite.
The ideas of number and the knowledge of the processes with abstract numbers that the student has gained in arithmetic are a proper and necessary introduction to his work in algebra; but since number is discussed in a more general way in algebra than in arithmetic, many arithmetical processes, terms and symbols.
Symbols of algebra are used to relate all variables and constants together. These symbols include;
• Multiply
* Multiply
/ Divide
+ Add or Positive
- Subtract or Negative
( ) Calculate what is inside of the parentheses first. (grouping symbols)