Question 1106850
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If the polynomial is to have real coefficients, then complex roots must occur in conjugate pairs.  Since -1+2i is a root, -1-2i must be another root.<br>
The linear factors are (x-5) and (x+3); the quadratic factor corresponding to the two complex roots is (x^2+2x+5).  The polynomial in standard form is then<br>
{{{(x-5)(x+3)(x^2+2x+5) = x^4-14x^2-40x-75}}}