If f(1) = 160 and f(n + 1) = –2f(n), what is f(4)?

F4 can be rewritten to:

f(4) = f(3+1) = -2f(3)    [Using f(n+1) = -2f(n)]

Keep using f(n+1):

-2f(3) = -2f(2+1) = -2[-2f(2)] = 4f(2)

Again:

4f(2) = 4f(1+1) = 4[-2f(1)] = -8f(1) = -8*160

-8*160 = -1280

Answer to your question: a. the fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. the roots are ​ x=1±i7√2 .number of roots=degree of polynomialhere, degree of polynomial is 2 so number of roots will be 2.hope it *_*