Question

Check all of the numbers that are potential rational roots of f(x) = x4 – 2x3 + 5x2 – 7x + 9.

Answer 1

The answer is a,b, and c. 1,3,9

Answer 2

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:

⇒$x^3 +\frac{bx^2}{a} +\frac{cx}{a}+\frac{d}{a}=0$

So, the roots will be, $\pm1, \pm d, \pm \frac{1}{a},\pm \frac{d}{a}$.

Now , the given polynomial having highest degree 4 is :

$f(x) = x^4 - 2x^3 + 5x^2 - 7x + 9.$

Constant Term =9

So, Possible Roots are = All integral factor of 9=$\pm 1, \pm 3, \pm 9$

Option (a) $\pm 1$ , Option (b)$\pm 3$  ,and Option (c)$\pm 9$ are correct options.