anonymous
  • anonymous
For each polynomial function, find all zeros and their multiplicities. f(x)=(7x-2)^3(x^2+9)^2
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Th\[(x+3i)^2=0 \rightarrow x=-3i\]e zeros are found when f(x)=0. Then,\[(7x-3)^3(x^2+9)^2=0\]Now, the second factor can be factored down further to,\[x^2+9=(x-3i)(x+3i)\]so \[f(x)=(7x-2)^3(x-3i)^2(x+3i)^2\]The function will be zero when any one of these factors is zero; that is, when,\[(7x-2)^3=0\rightarrow x=\frac{2}{7}\]\[(x-3i)^2=0 \rightarrow x=3i\]\[(x+3i)^2=0 \rightarrow x=-3i\]The multiplicity of the root is determined by the power of the factor from which the root came from. Your roots have multiplicity 3, 2 and 2 respectively.

Looking for something else?

Not the answer you are looking for? Search for more explanations.