Question

Find the value of m and n so that the polynomial f(x) = x3 – 6 x2 + mx – n is exactly divisible by (x-1) as well as (x-2)

Answer 1

Hi,I hope this is helpful to you
If f(x) =x^3-6x^2+mx-n is exactly divisible by x-1
So x-1=0
x=1
f(1)=1^3-6(1)^2+m×1-n=0
=1-6+m-n=0
=-5+m-n=0
=m=n+5 ... (1)
If f(x) =x^3-6x^2+mx-n is exactly divisible by x-2
So x-2=0
x=2
f(2)=2^3-6(2)^2+m×2-n=0
=8-24+2m-n=0
=-16+2m-n=0
=2m-n=16 ... (2)
From eq 1&2
2(n+5)-n=16[m=n+5]
2n+10-n=16
n=16-10
n=6
Putting the value of n in eq 1
m=6+5
m=11
#Ra12f

Answer 2

Answer:

Step-by-step explanation: