Question 1154820
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With the polynomial in standard form (in decreasing powers of the variable), there are 5 sign changes.  So the number of positive real roots is 5, or 3, or 1.<br>
Replacing "x" with "-x" in the polynomial results in a polynomial with 0 sign changes, so there are no negative real roots.<br>
A graph shows that in fact there are 3 positive real roots, which means there is 1 pair of imaginary roots.<br>
{{{graph(400,400,-2,4,-5,5,x^5-3x^4+x^3-4x^2+5x-1)}}}<br>