Types of Algebraic Equations:
The letters in algebraic equations are referred to as unknowns. Therefore, x is the unknown in the equation 3x + 5 = 8.
Algebraic equations can have any number of unknowns. The name unknown arises because letters are substituted for the numerical values which are not known in a problem.
The number of unknowns in a problem determines the number of equations required to solve for the numerical values of the unknowns. Problems including one unknown can be solved along with a single equation; problems including two unknowns need two independent equations, and many more.
The degree of an equation depends on the power of the unknowns. The degree of an algebraic word is equivalent to the exponent of the unknown. Therefore, the term 3x is a first degree term; 3x2 is a second degree term, and 3x3 is a third degree term. The degree of an equation is the similar as the highest degree term. Linear or first degree equations hold no terms higher than first degree. Therefore, 2x + 3 = 9 is a linear equation. Quadratic/second degree equations contain up to second degree terms, but no higher. Therefore, x2 + 3x = 6, is a quadratic equation. Cubic or third degree equations hold up to third degree terms, but no higher. Therefore, 4x3 + 3x = 12 is a cubic equation.
The degree of an equation determines the number of roots of the equation. Linear equations have one root and quadratic equations have two roots, and so on. In common, the number of roots of any equation is the similar as the degree of the equation.
An Exponential equation is those in that the unknown appears in the exponent. For instance,
e-2.7x = 290 is an exponential equation. Exponential equations can be of any degree.
The primary principle used in solving any algebraic equation is: some operation performed on one side of an equation must also be performed on the other side for the equation to remain true. That one principle is used to solve all kinds of equations.