Verified answer

the thing is:

if the a+b*i is an solution also a-b*i has to be an solution too

otherwise the coefficients would not be real

so the third zero has to be 4 + i

one thank you to freshen up a cubic is to look for integer innovations. by using actuality the synthetic from the roots of a cubic polynomial equals minus the consistent term, seem on the factors of 26: a million, 2, 13, 26. x=a million does not paintings, yet x=2 does. So 2 is one root. If 2 is a root, then our polynomial could be written indoors the style: (x-2)*( a quadratic). to locate the quadratic, do the long branch: (x^3-8x^2+25x-26)/ (x-2) = x^2 -6x +13. Now use the quadratic equation to freshen up this: you get x = [ 6 +/- sqrt(-sixteen) ]/2 = 3 +/- 2i. So the three roots of the cubic are 2, 3+2i, 3-2i. for this reason, we are in a position to jot down the polynomial in factored type as: (x-2)*[x-(3+2i)]*[x-(3-2i)].