Question 1088043
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Two zeros of a polynomial are 3-4i and 1+i. What is the lowest possible degree of the polynomial. I believe the quadratic equation would be x^2+xi-4x+5-i.
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Lowest possible degree for the polynomial is 4.  Why?  Complex zeros occur as conjugate pairs.


{{{(x-(3-4i))(x-(3+4i))(x-(1+i))(x-(1-i))}}}


Steps to simplify:
{{{(x-3+4i)(x-3-4i)(x-1-i)(x-1+i)}}}
{{{((x-3)+4i)((x-3)-4i)((x-1)-i)((x-1)+i)}}}
{{{((x-3)^2+16)((x-1)^2+1)}}}------used knowledge of difference of squares
{{{(x^2-6x+9+16)(x^2-2x+1+1)}}}
...continue simplifying and then doing the multiplication...
but you see the degree is 4
.
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