Question 1053141
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Find an nth degree polynomial function with real coefficients satisfying the given conditions. 
n=3; -4 and 6+5i are zeros; f(1)=250
My question is not exactly the answer to this problem. My question is what are 'i's, referring to 6+5i, and how they affect the entire problem. 
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1.  6+5i is the complex number.
    6 is its real part.
    5i is its imaginary part.
    i is that famous complex number ("imaginary unit") which is {{{i^2}}} = -1.

2.  The polynomials with real coefficients all have this remarkable property:
    if  a+bi is the root of such a polynomial, then the so named (so called) conjugate complex number a-bi is the complex root also.

3.  Since you ask such a question (of an introductory level), then I think 
    it might be useful for you to make acquaintance with complex numbers.

    You may use the lessons in this site:

    &nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/Complex-numbers-and-arithmetical-operations.lesson>Complex numbers and arithmetic operations on them</A>

    &nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/Complex-plane.lesson>Complex plane</A>

    &nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/Addition-and-subtraction-of-complex-numbers-in-complex-plane.lesson>Addition and subtraction of complex numbers in complex plane</A>

    &nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/Multiplication-and-division-of-complex-numbers-in-complex-plane-.lesson>Multiplication and division of complex numbers in complex plane</A>

    &nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/Raising-a-complex-number-to-an-integer-power.lesson>Raising a complex number to an integer power</A>

    &nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/How-to-take-a-root-of-a-complex-number.lesson>How to take a root of a complex number</A>

    &nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/Solution-of-the-quadratic-equation-with-real-coefficients-on-complex-domain.lesson>Solution of the quadratic equation with real coefficients on complex domain</A>

    &nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/Solution-of-the-quadratic-equation-with-complex-coefficients-on-complex-domain.lesson>Solution of the quadratic equation with complex coefficients on complex domain</A>

    &nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/Solved-problems-on-taking-roots-of-complex-numbers.lesson>Solved problems on taking roots of complex numbers</A>

    &nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/Solved-problems-on-arithmetic-operations-on-complex-numbers.lesson>Solved problems on arithmetic operations on complex numbers</A>
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