Rational Zero Theorem Help!

[SayWhat]

1. Why is it that, technically, we cannot use the Rational Zeroes Theorem to find the possible rational zeroes of P(x) = 1/324 * x^5 - 1/18?

2. What modification can we make to the function P(x) from the previous problem *without changing the outputs* so that we can find the possible rational zeroes using the Rational Zeroes Theorem?

 

[HallsofIvy]

When you saw that the problem referred to the "rational root theorem" did you not look that up in your text book? The rational root theorem says that if a polynomial with integer coefficients has a rational root, then it must be of the form x= p/q where q is an integer that evenly divides the leading coefficient and p is an integer that evenly divides the constant term.

 

[SayWhat]

So, the answer to number 2 would be: p(x): 324x^5-18 ?

 

[HallsofIvy]

No! You appear to have multiplied the coefficient of x^5 by 324^2= 104976 while multiplying 1/18 by 324. You can't do that and still have the same roots!

You can multiply both sides of \(\displaystyle 1/324 * x^5 - 1/18= 0\) by 324 to get \(\displaystyle x^5- 18= 0\) and you can apply the "rational root theorem" to that.