Using Rational root theorem
For any polynomial , ax³ + b x² + c x + d= 0,
To find the possible root , we convert the cubic equation as follows:
⇒[tex]x^3 +\frac{bx^2}{a} +\frac{cx}{a}+\frac{d}{a}=0[/tex]
So, the roots will be, [tex]\pm1, \pm d, \pm \frac{1}{a},\pm \frac{d}{a}[/tex].
Now , the given polynomial having highest degree 4 is :
[tex]f(x) = x^4 - 2x^3 + 5x^2 - 7x + 9.[/tex]
Constant Term =9
So, Possible Roots are = All integral factor of 9=[tex]\pm 1, \pm 3, \pm 9[/tex]
Option (a) [tex]\pm 1[/tex] , Option (b)[tex]\pm 3[/tex] ,and Option (c)[tex]\pm 9[/tex] are correct options.
