Question

Find a fourth-degree polynomial that has the indicated zeros: _ _
-2/5 (multiplicity 2), 3+/2, and 3-/2.

Answer 1

\[(5x+2)^2\] is one factor. that makes
\[-\frac{2}{5}\] a zero with multiplicity 2

Answer 2

the other factor is
\[(x-(3+\sqrt{2}))(x-(3-\sqrt{2}))\] so you have to multiply that out, which is easier than it looks. can you do it?

Answer 3

\[x^2-6x+7\]

Answer 4

?right?

Answer 5

yes!

Answer 6

so now if you need to you have to multiply
\[(x^2-6x+7)(5x+2)^2\] to put in standard form. if you need to