Question

How many sign changes are in the polynomial f(x) = 3x^3 - 7x^2 - 9x + 1
A. 0
B. 1
C. 2
D. 3

Answer 1

first find the roots of f(x)
can you do that?

Answer 2

i have no idea how to find roots and i cant find a calculator that works for me either. meh.

Answer 3

f(x) = 3x^3 -7x^2 -9x +1
= 3x^3+3x^2 -10x^2 -10x +x+1
= 3x^2(x+1)-10x(x+1)+1(x+1)
= (3x^2 -10x +1) (x+1)

Answer 4

so now what do i do with that ?

Answer 5

f(x) = {(3x^2 -10x +1)} (x+1)
= {3(x^2-10/3 x) + 1} (x+1)
= {3(x^2 - 2* x * 5/3 + (5/3)^2 -(5/3)^2 ) +1 } (x+1)
= {3(x-5/3)^2 -25/3 +1} (x+1)
= { 3(x-5/3)^2 -22/3} (x+1)

Answer 6

i guess i dont know what that means now.