Question

Give a possible formula for the 4th degree polynomial graphed below. Assume the graph crosses the x-axis at exactly −2, 2, and 5. Use k if your leading coefficient is positive and −k if your leading coefficient is negative.

http://www.webassign.net/hgmcalc5/1-6-012.jpg

I've tried:
-k(x^4)-7(x^3)+6(x^2)+28x-40
which I believe is the correct answer but i must be wrong! Thank you in advance!

Answer 1

So we have our polynomial roots, which must be:
\[
f(x)=0
\]At:
\[
x=\{-2,2, 5\}
\]And, for 2, the multiplicity is also two, so we put these in a polynomial to find:
\[
k(x+2)(x-2)^2(x-5)=f(x)\\
k\in\mathbb{R}^+
\]Which, when multiplied out is:
\[
k(x^4-7 x^3+6 x^2+28 x-40)=f(x)
\]But, it stated one example, so if we make \(k=1\), then:
\[
f(x)=x^4-7 x^3+6 x^2+28 x-40
\]Which, is your answer without the leading constant.

Answer 2

Huh, than you I thought I was right. I resubmitted that as the answer and it stil counted it as wrong. Something must be up with the way i submitted it or something is wrong with the coding. Thank you though!

Answer 3

Sure thing.