SOLUTION: What is the simplest polynomial function with the given zeros, 2i, -3?

Question 1159703: What is the simplest polynomial function with the given zeros, 2i, -3?
Found 2 solutions by ikleyn, solver91311:
Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
.

p(x) = (x-2i)*(x+3)

Notice that the word "simplest" is not a Math term.

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Tutor @solver91311 teaches you that

        "Complex zeros always appear in conjugate pairs, therefore if is a zero, must also be a zero."

It is NOT ALWAYS TRUE.

It is true, if the polynomial has real coefficients - - - but the problems SAYS NOTHING about it;

so, there is NO RATIONALE for such a statement.

         * * * " incontrovertibly correct answer to the question "   ?   * * * - - - Ha - ha - ha. * * *

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Complex zeros always appear in conjugate pairs, therefore if is a zero, must also be a zero. Real zeros have no such restriction, so the simplest polynomial with the given zeros has exactly three zeros, and is a 3rd-degree polynomial.

If is a zero of a polynomial function then is a factor of the polynomial. Hence, your desired polynomial function, in factored form is:

While the above is incontrovertibly a correct answer to the question, I suspect that you will need to present the answer in standard form, namely:

And this will require that you multiply the three factors together and collect like terms. Hint: The product of two conjugate binomials is the difference of two squares. Don't forget that . I'll leave the rest in your capable hands.

John

My calculator said it, I believe it, that settles it

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