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Determine whether each of the following statement is always, sometimes,
or never true.
27. A polynomial function with real coefficients has real zeros.
28. Polynomial functions with complex coefficients have one complex zero.
29. A polynomial function that does not intercept the x-axis has complex roots only

Question

HELPPPPPPPPPPPPPPPPPPPPP I WILL GIVE A MEDAL!!!!!!!!!!!!!!!!!!!!

Determine whether each of the following statement is always, sometimes,
or never true.
 27. A polynomial function with real coefficients has real zeros.
 28. Polynomial functions with complex coefficients have one complex zero.
 29. A polynomial function that does not intercept the x-axis has complex roots only

anonymous · Answer

27 is sometimes true. x^2 = 1 has real coefficients (the 1 on the x^2 term) and has 2 real solutions (1 and -1). However, x^2 = -1 also has real coefficients but has no real solutions.
28 is never true. There's a rule (sorry but I forgot what it was) that states that if there is a complex root, there is always a match with its complex conjugate. There can only ever be an even number of complex roots.
29 is always true. If a function has a graph, it has values, but the intersections with the x-axis are the real solutions. If it has no intersections, there are no real solutions.