Question 1210413
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Find a degree 3 polynomial with real coefficients having zeros 1 and 4i and a lead coefficient of 1. 
Write P in expanded form. Be sure to write the full equation, including P(x) =.
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<pre>
If a polynomial with real coefficients has a root which is a complex number, 
then this polynomial has another root which is the conjugate complex number.


It is a general property of polynomials with real coefficients.  
In our case, it means that the seeking polynomial has the roots  4i,  -4i  and  1.


Hence, the seeking polynomial is

    P(x) = (x-1)*(x-4i)*(x-(-4i)) = (x-1)*(x^2+16) = x^3 - x^2 + 16x - 16.


<U>ANSWER</U>.  P(x) = x^3 - x^2 + 16x - 16.
</pre>

Solved.