MATHEMATICS ENCYCLOPEDIA

When we say collection of objects is listed in a sequence, we usually mean that the collection is ordered in such a way that it has an identified first member, second member, third member and so on. The numbers occuring in a sequence are called its terms. The nth term is called the general term of the sequence. If a, b, c, d,......be in a sequence , then the expression a + b + c + d + ..........    is called the series associated with the given sequence. Sequences following specific patterns are called progressions.

Definition of quadratic equation: A quadratic equation in the variable x is an equation of the form ax^2 + bx + c = 0, where a, b, c are real numbers, and a is not equal to zero, e.g. 6x^2 - x - 2 = 0. In fact, any equation of the form p(x) = 0, where p(x) is a polynomial of degree 2, is a quadratic equation. A real number α is called the root of the quadratic equation ax^2 + bx + c = 0, if aα^2 + bα + c = 0. The roots and zeroes of the quadratic equation ax^2 + bx + c = 0 are the same thing. Standard form of the quadratic equation is ax^2 + bx + c = 0, and a is not equal to zero. If b^2 - 4ac >= 0, then the roots of the quadratic equation ax^2 + bx + c = 0 are given by the formula given in the picture.  Discriminant: Since b^2 - 4ac determines whether the quadratic equation has real roots or not, b^2 - 4ac is called the discriminant of the quadratic equation. A quadratic equation has: two distinct real roots, if b^2 - 4ac > 0, two equal real roots, if b^2 - 4ac