Math, asked by parthajit7052, 8 months ago

in a theatre, people are sitting in rows. If f(x) = x4+ 3x3+3x2+ ax +b represents the total number of people in the theatre and g(x) = x2+ 5 represents the number of people sitting in each row, then find number of rows in each class. Also find the value of a and b.

Answers

Answered by amitnrw
2

Given  : people are sitting in rows.

f(x) = x⁴+ 3x³+3x²+ ax +b represents the total number of people in the theatre

g(x) = x²+ 5

To Find : number of rows

value of a and b.

Solution:

                  x² + 3x - 2

x²+ 5      _|  x⁴+ 3x³+3x²+ ax +b  |_

                   x⁴ +    +  5x²

                 __________

                        3x³ - 2x²+ ax +b

                        3x³        + 15x +b

                      ______________

                               - 2x²+ (a-15)x +b  

                               -2x²               -10

                              _______________

                                        (a-15)x + b + 10

     (a-15)x + b + 10  = 0

=> a - 15 = 0  => a = 15

  b + 10 = 0 => b = -10

x² + 3x - 2  is number of Rows

value of a = 15

Value of b = - 10

Another method :

f(x) = x⁴+ 3x³+3x²+ ax +b  

g(x) = x²+ 5

substitute  x²+ 5  = 0 => x² = - 5 and Equate f(x) = 0

25 -15x  -15 + ax + b = 0

=> (a -   15)x  + (10 + b) = 0

=> a = 15 , b = -10

f(x) = x⁴+ 3x³+3x²+ 15x  - 10

Then divided by = x²+ 5

x⁴+ 3x³+3x²+ 15x  - 10 = (x²+ 5 )(x²+ 3x - 2)

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