Question

If a polynomial with real coefficients is of degree 3. Can we say there must be at least 1 real root?a. Yes, because complex roots must appear in conjugate pairs, leaving one root real. b. No. we can’t say anything about this casec. Yes, because if there is one real root, there must be two additional real rootsd. No, because such a curve never crosses the x-axise. Sometimes yes and sometimes no

Answer 1

If we have a polynomial odf degree 3 it must have 3 roots

And one of then should be real the answer is true

And the correct choice is:

a. Yes, because complex roots must appear in conjugate pairs, leaving one root real.

Since we have two possible options:

1) (x-i)(x+i) (x-a) with 2 factors conjugate and 1 root real a and two other complex numebrs

2) (x-a)(x-b)(x-c) with 3 real roots a,b and c

So then we must have at least one root assuming that the coeffcients of the polynomial are not complex