0
$\begingroup$

The polynomial

$F(x) = x^5-9x^4+24x^3-24x^2+23x-15$

has roots $x=1$ and $x=j$. Calculate all the roots of the polynomial.

I was told I had to use radicals or similar to solve this but after reading up on it I'm still confused about how to solve it.

  • 0
    If you don't want to factor, then you can assume $F(x) = (x-1)(x-j)(x+j)(x-a)(x-b).$ Expand $F(x),$ equate with $x^5-9x^4+24x^3-24x^2+23x-15,$ and solve for $ab.$ *Sanity check: $a^2+b^2=34.$*2012-01-08

3 Answers 3