According to the Rational Root Theorem, which number is a potential root of f(x) = 9x8 + 9x6 – 12x + 7?
Accepted Solution
A:
Answer:[tex]\pm 1, \pm\dfrac{1}{3},\pm\dfrac{1}{9},\pm 7, \pm\dfrac{7}{3},\pm\dfrac{7}{9}[/tex].Step-by-step explanation:According to the Rational Root Theorem, the potential roots of a polynomial are[tex]x=\pm\dfrac{p}{q}[/tex] where, p is a factor of constant and q is a factor of leading term.The given polynomial is[tex]f(x)=9x^8+9x^6-12x+7[/tex]Here, 9 is the leading term and 7 is constant.Factors of 9 are ±1, ±3, ±9.Factors of 7 are ±1, ±7.Using rational root theorem, the rational or potential roots are [tex]x=\pm 1, \pm\dfrac{1}{3},\pm\dfrac{1}{9},\pm 7, \pm\dfrac{7}{3},\pm\dfrac{7}{9}[/tex]Therefore, the potential root of f(x) are [tex]\pm 1, \pm\dfrac{1}{3},\pm\dfrac{1}{9},\pm 7, \pm\dfrac{7}{3},\pm\dfrac{7}{9}[/tex].