Understanding Real Roots of a Polynomial

The video tutorial explores the possible number of real roots for a 7th degree polynomial. It explains that according to the Fundamental Theorem of Algebra, there are 7 roots in total, some of which can be real. The video discusses the impossibility of having an odd number of non-real complex roots, as they come in conjugate pairs. It concludes that the possible number of real roots for the polynomial are 7, 5, 3, or 1.

What is the degree of the polynomial discussed in the video?

• 5th degree

• 7th degree

• 6th degree

• 8th degree

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CCSS.HSN.CN.C.9

According to the Fundamental Theorem of Algebra, how many roots does a 7th degree polynomial have?

• 5 roots

• 6 roots

• 8 roots

• 7 roots

Why can't a 7th degree polynomial have 8 real roots?

• Because it can only have 4 real roots

• Because it can only have 5 real roots

• Because it can only have 6 real roots

• Because it can only have 7 roots in total

Why is it impossible for a 7th degree polynomial to have 6 real roots?

• Because it can only have 5 real roots

• Because it can only have 3 real roots

• Because non-real roots must come in pairs

• Because it can only have 4 real roots

What is the minimum number of real roots a 7th degree polynomial can have?

• 1 real root

• 0 real roots

• 2 real roots

• 3 real roots

What pattern is observed in the number of real roots a 7th degree polynomial can have?

• It can only have 7 real roots

• It can have any number of real roots

• It can only have an even number of real roots

• It can only have an odd number of real roots

Why can't a 7th degree polynomial have 0 real roots?

• Because non-real roots must come in pairs

• Because it must have 7 real roots

• Because it must have at least 1 real root

• Because it must have 5 real roots

What is the maximum number of real roots a 7th degree polynomial can have?

• 8 real roots

• 6 real roots

• 5 real roots

• 7 real roots

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CCSS.HSN.CN.C.9

If a 7th degree polynomial has 3 real roots, how many non-real roots does it have?

• 2 non-real roots

• 3 non-real roots

• 5 non-real roots

• 4 non-real roots

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CCSS.HSN.CN.C.9

Which of the following is a possible combination of real and non-real roots for a 7th degree polynomial?

• 2 real and 5 non-real

• 3 real and 4 non-real

• 4 real and 3 non-real

• 6 real and 1 non-real

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CCSS.HSN.CN.C.9