Question

If f (y)=(y^4)-4 (y^3)+8(y^2) -my + n is divided by y+1 and y-1, we get remainders as 10 and 16 respectively. Find the values of m and n

Answer 1

Answer:

m=-4

n=7

Step-by-step explanation:

For y+1

(y^4)-4 (y^3)+8(y^2) -my + n=10

put the value of y= -1

((-1)^4)-4 (-1^3)+8(-1^2) -m(-1) + n=10

1-4(-1)+8*1+m+n=10

1+4+8+m+n=10

13+m+n=10

m+n=-3.......(A)

For y-1

(y^4)-4 (y^3)+8(y^2) -my + n=16

put the calue of y=1

(1^4)-4 (1^3)+8(1^2) -m1 + n=16

1-4+8-m+n=16

5-m+n=16

-m+n=11........(B)

solve equation A and B

A+B

(m+n)+(-m+n)=11+3

m+n-m+n=14

2n=14

n=14/2

n=7..........................Answer(1)

put the value of n in A

m+n=3

m+7=3

m=3-7

m=-4...................Answer(2)