Without the knowledge of algebra, it would rather be difficult or impossible to solve many practical problems in day to day life. The principal instrument for solving problems in algebra is the equation. Many problems that arise in science and technology we encounter equations. We have already learnt about linear and quadratic equations. We now try to learn about the equations of degree higher than two. We also learn some elementary properties in the general theory of equations.
¤ An equation f(x) = 0 is said to be an algebraic equation or a polynomial equation or an equation of degree 'n' (n > 0), if f(x) is a polynomial of degree 'n'.
¤ A complex number α is said to be a root of the equation f(x) = 0 if f(α) = 0.
¤ Let f(x) = a₀xⁿ + a¹x^n-1 + a₂ x ^n-2 + . . . + a_n = 0 be an algebraic equation.

    If the coefficients are real then f(x) = 0 is called an algebraic equation with real coefficients.
¤ Every algebraic equation of non zero degree has a root.
¤ Every algebraic equation of degree n has n roots and no more.

A root α of an algebraic equation f(x) = 0 is said to be a multiple root of order m if it occurs
m times.
A multiple root α of order m of f(x) = 0 is a multiple root of order m-1 of f1(x) = 0 where f¹(x) is the derivative of f(x).

¤ If α₁, α₂ .... αn are the roots of an algebraic equation f(x) = 0 of degree 'n' then 
                    f(x) = (x - α₁) (x - α₂) . . . (x - α_n) = 0