positive numbers

In the given trinomial expression if all terms are positive, then both the factors are positive..

We know that 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2 6 Here 2 is called the base and 6 is called the power (or index or exponent). We say that "64 is equal to base 2 raised to the power 6". The Laws of Indices are : Product Law, Quotient Law, Power Law, (ab) m = a m . b m . An irrational root of a ..

If the middle term is negative, and last term is positive, signs of both the factors will be negativ..

An algebraic expression of the form a 0 +a 1 x+a 2 x 2 +.+a n x n where a 0 , a 1 , a 2 ,.a n are real numbers, n is a positive integer is called a polynomial in ..

If x and y are real numbers, then x + iy is called a complex number. x is called the real part and y is called the imaginary part. The complex number x + iy is also written as an ordered pair (x, y) and is denoted by z. i.e., z = x + iy The positive value is ..

The general form of the trinomial is (x 2 + cx + d) where c and d have different numerical values: c = a + b, and d = ab. In the given trinomial expression if all terms are positive, then both the factors are positive. If the middle term is negative, and last ..

Matrices - Consider the arrangement In this arrangement, there are two rows and four columns. The number 3 lies in the 2 n d row and 4 t h column. Each number has a fixed position. Matrix A has 2 rows and 3 columns and is thus of order 2 x 3. Matrix B has 3 rows and 2 ..

Argand diagram of the q th roots of a Complex number - All the q-th roots of z lie on a circle centred at the origin O and having radius equal to the real, positive q t h root of r. One of them has amplitude and others are uniformly spaced around the circle separated from others..

>These formulae are used when 'last term' is given. (v) If 'a' and 'r' be the first term and common ratio of a G.P. such (vi) If the sequence a, G 1 , G 2 ,....,G n , b of positive numbers is a G.P., then the numbers G 1 , G 2 ,....,G n , are called the n geometric mea..

All the q-th roots of z lie on a circle centred at the origin O and having radius equal to the real, positive q t h root of r. One of them has amplitude q /q and others are uniformly spaced around the circle separated from others by an angle 2p ..