Question

please ans this with corre solution
it's urgent

Answer 1

Hi dear 

In order to find the value of  m and n so that 

f(x) = x³ - 6x² + mx  - n  is exactly divide by (x -1) and (x - 2) 

it means ( x -1 ) and (x -2) are factors of f(x) 

and when the value of x put in f(x) it will result in zero 

ATQ 

taking (x -1) as factor 

f(1) ≡ 1³ - 6(1)² + m(1) - n = 0 

                    1 - 6 + m - n  = 0 

                     m - 5 - n       = 0 ___________(1)

Taking (x -2) as factor 

f(2) ≡ 2³ - 6(2)² + m(2)  - n = 0 

                  8 - 24 + 2m - n = 0 

                        2m - 16 - n = 0 ______(2)

subtracting (1) from (2) 

m - 11 = 0 

m = 11 

also , 
 putting value of m in equation 1 we get , 

11 - 5 - n = 0 

- n = -11 + 5 

- n = - 6 

n = 6