Ace school

with brainly

  • Get help from millions of students
  • Learn from experts with step-by-step explanations
  • Level-up by helping others

A community for students.

T or F any 3rd degree polynomial has at at least one real root?

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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.

Join Brainly to access

this expert answer

SEE EXPERT ANSWER

To see the expert answer you'll need to create a free account at Brainly

True, can you explain why?
True
Yeah @timo86m , but the third degree polynomial should have real coefficients

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

yes i can @cherylim23 because x^2 has u or n shape but 3rd degree has a |dw:1342235273380:dw| shape
Condition i s that all coefficients are real. Do you know why? This relates back to the fundamental theorem of algebra, which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. However, if the coeffients are all real, you can apply the complex conjugate theorem here, leaving you definitely one real root at least since all complex roots would have occured in conjugate pairs. Bit hard to understand if you haven't learnt complex numbers yet, but just keep this in mind
i know basic complex numbers like a HS level knowledge of them. But I know if it is all real then a shape like |dw:1342235527228:dw| should always intersect the x axis at least once. in a u or n shaped graph due to a 2nd dagree polynomial there are ways to shift the curve up or down so that it never intersects the x axis.
another reason is that the complex roots come in conjugate pairs, so you cannot have just one of them or three of them
good point

Not the answer you are looking for?

Search for more explanations.

Ask your own question