Does every polynomial equation have at least one real root? a. Why must every polynomial equation...

Does every polynomial equation have at least one real root?

a. Why must every polynomial equation of degree 3 have at least one real root?

b. Provide an example of a polynomial of degree 3 with three real roots. How did you find this?

c. Provide an example of a polynomial of degree 3 with only one real root. How did you find this?

Expert Solution

No, every polynomial need not have a real root.

(a) Yes,any polynomial of degree 3 must have at least one real root. Since complex roots appear in pair, thus, any polynomial of degree 3 can have either 2 complex roots or zero complex roots. Thus, it must have at least one real root.

(b) is a polynomial with three real roots. We choose all the roots in real.

(c) is a polynomial with one real and two complex roots since has no real roots

milcah answered 2 years ago

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