e math algebra elementary

If any number is added to both sides of an equation, then the equality of the equation remains unchanged. i.e., if x = y then x + a = y ..

Without solving the quadratic equation, the nature of the roots can be determined using the discriminant. i) D >0 i.e., positive and not a perfect square. The roots are real and distinct (irrational). ii) D >0 i.e., perfect square. The roots are rational and distin..

Nature of the roots - Without solving the quadratic equation, the nature of the roots can be determined using the discriminant. i) D >0 i.e., positive and not a perfect square. The roots are real and distinct (irrational). ii) D >0 i.e., perfect square. The roots are ratio..

An equation of one variable and of first order (i.e., its highest power is one) is called a linear equation . Such an equation has only one solution. A solution is also called the 'root' of the given equatio..

Multiplying by 4 times the coefficient of x 2 on both sides i.e., 4..

If a o 0, then the polynomial P(x) or f(x) is of degree 'n' i.e., it is the highest power of the variable x in the rational and integral polynomial. A polynomial of degree 2 is called a quadratic polynomia..

When the coefficient of the highest power is 1. i.e., ax 2 bx c, when a = 1 and b and c are integers. When two binomials are multiplied the product is a trinomial. Thus (x + 4) (x + 5) = x 2 + 9x + 20 (1) (x - 4) (x - 5) = x 2 - 9x + 20 (2) In this chapter we try to express ..

a) "x is less than y" b) " x is greater than y" c) "x is multiple of 3" d) "x divides y" e) "Cube of x plus the square of y is 25" f) "Triangle x is congruent to triangle y..

A relation which is reflexive, symmetric and transitive is called the Equivalence relation. i.e., A relation R in a set A is called equivalence if it satisfies the following conditions. ..

1. i) Upto step 6 in the I Method and upto Step 7 in the II Method, gives the process of completing the square. ii) The quadratic equation has two roots. (i.e., there are two values for x) is b 2 - 4ac. This is usually denoted by D or D. D determines the nature of the roo..