Question

What is the value of m such that x ^2 − x − 1 is a factor of mx^7 + nx^6 + 1? Here m and n are integers.

Answer 1

Answer:

m=0, n= -1

Step-by-step explanation:

x^2-x-1=0

x^2-x+x-1=0

x(x-1)+1(x-1)=0

(x+1)(x-1)=0

x-1=0 or x+1=0

x=1 , x= -1

mx^7+nx^6+1=0

x=1

m+n=-1

mx^7+nx^6+1=0

x= -1

-m+n =-1

n= -1 ,m=0