example

22
Jul
Examples

(1) What should be added to 3x2 – 5x + 9   to get  x2 – 2x – 3  ?

Soln. Let,  3x2 –  5x  +  9   +  p(x)  =   x2 –  2x  –  3

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22
Jul
Results on Rational Expressions

Results on Rational Expressions  :  

(i) Sum ( or difference or product ) of  two rational expressions is a rational expression.

(ii) Rational expressions satisfies commutative, associative and distributive laws.

(iii) 0 …

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22
Jul
Rational  Expression

Rational  Expression  :   An expression of  the form \frac{p(x)}{q(x)} ,  where  p(x)  and  q(x)  are a polynomials and  q(x)

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22
Jul
Rational Expression

Degree and Coefficient  :   The highest index of  the given polynomial is called the degree of  the polynomial and the coefficient of  highest index term is called the coefficient of  the given polynomial.

 e.g….

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22
Jul
Examples 11 and 12

(11) Find  the set of  values of  k  for which 2x2 + 20x + k  can be factorized into real linear factors.

Soln. 2x2 + 20x + k  will be factorizable only when  D

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22
Jul
Examples 7 to 9

(7) Find the values of  m  for which  16x2 + mx + 9 = 0 has both equal roots.

Soln. For  equal  roots,  we  must have

D  =  0.

\therefore

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22
Jul
Examples 4 to 6

(4) Discuss the nature of the roots of the following equations :

(i) 4x2  +  15x  –  25  =  0

(ii) 4x2  –  12x  +  1  =  0

(iii) 9x2  +  6x  +  1  = …

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