f(x), g(x) are nonzero polynomials and f ( x 2 + x + 1 ) = f ( x ) g ( x ). Show that f(x) has even degree.

Question

f(x), g(x) are nonzero polynomials and   f  (      x    2    +  x  +  1  )  =  f  (  x  )  g  (  x  ). Show that f(x) has even degree.

Antwan Wiley · Accepted Answer

Step 1So your confidence interval is a confidence interval for the mean, but what we&#039;re looking for in this question is the confidence interval of the variance. In order to find that, we need to use the fact that for a normally distributed sample, the variance follows a chi-squared distribution.Step 2Because the sample size is 25, we know that   24                    s        2                    σ        2             follows a chi-squared distribution with   25  −  1  =  24 &quot;degrees of freedom&quot; (that is,   ν  =  24). Using a table (or a calculator), construct a 95% confidence interval about the mean of a   ν  =  24 chi-squared distribution, and solve for       s    2   to construct the confidence interval for the variance,       s    2  .For this problem, the confidence interval you should have is  0.0177  &amp;lt;      σ    2    &amp;lt;  0.0561

f(x) , g(x) are nonzero polynomials and f(x^2+x+1)=f(x)g(x). Show that f(x) has even degree.

Answered question

Answer & Explanation

New Questions in Precalculus