Parin

Parin Sir > Parin
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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22
Jul
Examples 1 to 3

Examples  :

(1) Solve  the equations :

(i) 3x2  +  5x  +  2  =  0

(ii) 3x2  –  5x  +  2  =  0

(iii)  3x2  +  5x  –  2  =  0

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22
Jul
To  form a Quadratic Equation

☼ To  form a Quadratic Equation :–   A quadratic equation whose roots are \alpha1  and 

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22
Jul
Some  important  expressions

☼ Some  important  expressions :–   We  know  that,

\alpha + \beta = - \frac{b}{a}

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22
Jul
Methods to solve Quadratic  Equation

☼ Methods to solve Quadratic  Equation  :   There are three different methods to solve the quadratic equation.

 (i) Method of  Factorization

  e.g. Solve  :  4 x2 – …

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22
Jul
Types  of   roots  of  a  Quadratic  Equation

☼ Types  of   roots  of  a  Quadratic  Equation  :   There are four different types of  roots associated with a Quadratic Equation.

(i) Rational  and  Distinct

e.g. Solve  :  3 x2 +…

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19
Jul
Quadratic Equation

…

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19
Jul
Index
  1. Polynomial  
  2. Equation  
  3. Simple  Equations
  4. …
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19
Jul
Examples 11 to 15

(11) A father is now five times as old as his son. Five years ago, he was nine times as old as his son. Find their present ages.

Soln. Let age of  the father  =  x  and that of  the son =  y

We are given that, x  =  5y         …

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