Can somebody explain how I find the potential roots of this function?
p(x) = x^4 + 22x^2 – 16x – 12

1 Answer

  • Rational root theorem. Find all the factors of the leading term's coefficient and the constant term; these are 1 and -12, respectively.

    1 has only one factor: 1 (call this [tex]n[/tex])

    -12 has a few more: [tex]\pm1,\pm2,\pm3,\pm4,\pm6,\pm12[/tex] (call these [tex]m[/tex])

    Potential roots will take on the form [tex]\dfrac mn[/tex], which means you can check these as possible roots: [tex]\pm1,\pm2,\pm3,\pm4,\pm6,\pm12[/tex]

    Plug each of these into [tex]p(x)[/tex]. If [tex]p\left(\dfrac mn\right)=0[/tex], then [tex]\dfrac mn[/tex] is a root.

    Unfortunately, you'll find none of these work, so this polynomial doesn't have any rational roots (which means finding any could be very tough).