Surd
An irrational root of a positive rational number is called a surd. Consider a number with base 'a' as a positive rational number with power of a fraction, say then Since is an n t h root, it is called a surd of order n, if it is irrational. e.g., (i) is a surd of orde..
An irrational root of a positive rational number is called a surd. Consider a number with base 'a' as a positive rational number with power of a fraction, say then Since is an n t h root, it is called a surd of order n, if it is irrational. e.g., (i) is a surd of orde..Type (ii) By expressing the polynomial as the difference of two squares
121x 2 - 25y 2 = (11x) 2 - (5y) 2 = (11x + 5y) (11x - 5y) [Using the identity a 2 -b 2 =(a-b)(a+b)] Factorise: (5a + 6b) 2 - 49b 2 Let x = 5a + 6b Then the given expression = (x) 2 - (7b) 2 = (x + 7b) (x - 7b) Re-substituting the value of x, we get = [(5a + 6b + 7b)] [(5a +..
121x 2 - 25y 2 = (11x) 2 - (5y) 2 = (11x + 5y) (11x - 5y) [Using the identity a 2 -b 2 =(a-b)(a+b)] Factorise: (5a + 6b) 2 - 49b 2 Let x = 5a + 6b Then the given expression = (x) 2 - (7b) 2 = (x + 7b) (x - 7b) Re-substituting the value of x, we get = [(5a + 6b + 7b)] [(5a +..Algebraic identity
An algebraic identity is a statement of equality between two algebraic expressions, but it is satisfied for all values of the variabl..
Summary
Every polynomial is continuous. Every rational function is continuou..
Factorization
If a polynomial can be written as the product of two or more expressions, then each expression is called the factor of the given polynomial.If a polynomial can be written as the product of two or more expressions, then each expression is called the factor of ..
The degree of a polynomial
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..
Linear inequations
An inequation is said to be linear if each term of the algebraic expression (or expressions) of the inequation contains first degree variables (not the product of variables..
Trinomials
Expressions of the form ax 2 + bx + c are called trinomialsExpressions of the form ax 2 + bx + c are called trinomi..
b)
Limit of a rational function can be found by substitution, if the limit of the denominator is not zero. In other words, where P(x) and Q(x) are polynomials, then we have ..
Limit of a rational function can be found by substitution, if the limit of the denominator is not zero. In other words, where P(x) and Q(x) are polynomials, then we have ..Some Basic Definitions
Notation: Usually a polynomial is denoted by P(x) and if k is any number then P(k) denotes the value of P(x) at x=k. The degree of a polynomial: 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..
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