SOLUTION: 1. Given f(x)=3x^4 -2x^3 + 7x -2, how many sign changes are there in the coefficient of f(-x)?

Algebra ->  Functions -> SOLUTION: 1. Given f(x)=3x^4 -2x^3 + 7x -2, how many sign changes are there in the coefficient of f(-x)?       Log On


   

Question 1189334: 1. Given f(x)=3x^4 -2x^3 + 7x -2, how many sign changes are there in the
coefficient of f(-x)?
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Given f%28x%29=3x%5E4+-2x%5E3+%2B+7x+-2,
..........signs: + - + -
how many sign changes are there in the coefficient of f%28-x%29?
f%28-x%29=3%28-x%29%5E4+-2%28-x%29%5E3+%2B+7%28-x%29+-2
f%28-x%29=3x%5E4+%2B2x%5E3+-+7x+-2
..........signs:+ + - - => compare to f%28x%29 and you see that second sign changes from - to +, third sign changes from + to -
so, two sign changes are there

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


I think the other tutor answered the wrong question....

The given function is

f%28x%29=3x%5E4-2x%5E3%2B7x-2

Replacing x by -x, we get

f%28-x%29=3%28-x%29%5E4-2%28-x%29%5E3%2B7%28-x%29-2
f%28-x%29=3x%5E4%2B2x%5E3-7x-2

In that function, the signs of the terms are +,+,-,-. There is only one sign change IN THAT FUNCTION.

Comparing the functions f(x) and f(-x), we see that two signs changed from one to the other. That is obvious, because from f(x) to f(-x) the sign will change on every term with an odd power.

But that is not what the question is about....