Please help me! Write a polynomial of degree 4 with zeros 3i, and -2 (multiplicity 2). Expand it out.

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.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

Please help me! Write a polynomial of degree 4 with zeros 3i, and -2 (multiplicity 2). Expand it out.

Mathematics
See more answers at brainly.com
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.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

If a polynomial has a zero at -2 that means one of our solutions is:\[\large\rm x=-2\]Adding 2 to each side gives us,\[\large\rm (x+2)=0\]Our 4th degree polynomial will contain this as one of it's factors. Since this zero has a multiplicity of 2, it will show up twice in our polynomial.\[\large\rm (x+2)(x+2)=0\]Ok we're half way there!
3i is a zero, same idea,\[\large\rm x=3i\]\[\large\rm (x-3i)=0\]So we can add this factor to our polynomial that we're constructing,\[\large\rm (x+2)(x+2)(x-3i)=0\]
Recall that `complex zeros` always come in conjugate pairs. So if 3i is a zero of this polynomial, then -3i is also a zero.\[\large\rm x=-3i\]\[\large\rm (x+3i)=0\]Adding the last factor to our polynomial gives us\[\large\rm (x+2)(x+2)(x-3i)(x+3i)=0\]

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

And then you have to expand out all of that madness :p
Wow, great explanation zepdrix. I appreciate your work :)

Not the answer you are looking for?

Search for more explanations.

Ask your own question