Write a polynomial with the degree of 3 that has rational coefficients, a leading coefficient of zero and has zeros of -3 and 1-7i

Question

Has to be in standard form

please help!!!

Answer 1

Hi there!

First, degree 3 means that the final form of the polynomial will have a variable with a highest power of 3. For example, x^3.

Second, when the zeros (also known as roots or solutions) are given, simply plug in each zero to the following (x-r). For example, if the zero given is 1, you would have (x-1); if the zero given is -1, you would have (x+1).

Third, every single "zero" that is complex always has a conjugate. For example, if you are given 3+2i, you also automatically have 3-2i. This then would be put into the (x-r) expression. So you would have (x-(3+2i)) and (x-(3-2i)).

Fourth, for your own problem, it would look like this: (x+3)((x-(1-7i))(x-(1+7i)).

Finally, to get the final answer, you would need to distribute (multiply) the entire expression together. By listing the highest exponents first, you will arrive at your answer in standard form.

-Justin

Answer 2

If the leading coefficient is ZERO, wouldn't that make the polynomial a degree of 2?