Question

if the polynomial x³ +mx² nx +6 has (x-2)as a factor and leaves remainder 3 ,when divided by x-3 'find the value of 'm' and 'n'​

Answer 1

p(x) = x^3 + mx^2 +nx + 6

p(2) = 8 + 4m + 2n + 6 = 4m+2n+14

=> 4m+2n+14= 0

=>2m +n+7=0

p(3)=27+9m + 3n +6 = 9m + 3n+33

=>9m + 3n +33 = 3

=>9m+ 3n+30 = 0

=>3m+n+10 = 0

solving equation gives-

3m+n+10 - (2m+n+7)= 0

=>m= -3

&

(2m+n+7)= 0

=>-6+n+7 =0

=>n= -1

Answer 2

Answer:

3m+n+10=0

solving equations given

3m+n+10-(2m+n+7)=0

m= -3 and

(2m+ n+ -7=0

6+n+7=0

n= -1