Question 1157331
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The polynomial is to have real coefficients, so the complex zeros occur in conjugate pairs.  So the roots are 3+2i, 3-2i, -5, and -5.<br>
Use Vieta's theorem to find the quadratic polynomial with roots 3+2i and 3-2i:
{{{(3+2i)+(3-2i) = 6}}}
{{{(3+2i)(3-2i) = 9-(-4) = 13}}}<br>
The quadratic polynomial is<br>
{{{x^2-6x+13}}}<br>
The quadratic polynomial with roots -5 and -5 is<br>
{{{x^2+10x+25}}}<br>
The polynomial we want is<br>
{{{f(x) = (x^2-6x+13)(x^2+10x+25) = x^4+4x^3-22x^2-20x+325}}}<br>