Answer:
The correct option is A.
Step-by-step explanation:
The question is:
According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 – 2x4 + 9x3 – x2 + 12?
A).f(x) = 3x5 – 2x4 – 9x3 + x2 – 12
B).f(x) = 3x6 – 2x5 + 9x4 – x3 + 12x
C).f(x) = 12x5 – 2x4 + 9x3 – x2 + 3
D).f(x) = 12x5 – 8x4 + 36x3 – 4x2 + 48
Solution:
The function given to us is:
3x5 – 2x4 + 9x3 – x2 + 12
Find the factors of 12 and consider it as 'p'
The factors of 12 are:
p = +/- 1 , +/-2 , +/-3 , +/- 4 , +/-6
Now find the factors of 3 and consider it as 'q'
The factors of 3 are:
q = +/- 1 , +/- 3
We know that we write rational terms in p/q form.
Therefore the Rational roots are given by p/q
+/- 1 , +/-2 , +/-3 , +/- 4 , +/-6 , +/- 1/3 , +/- 2/3 , +/- 4/3
Now we will solve the first function given in part A.
f(x) = 3x^5 – 2x^4 - 9x^3 + x^2 - 12
Again find the factors of 12 and consider it as 'p'
The factors are:
p = +/- 1 , +/-2 , +/-3 , +/- 4 , +/-6
Now find the factors of 3 and consider it as 'q' .
q = +/- 1 , +/- 3
Rational root are given by p/q
+/- 1 , +/-2 , +/-3 , +/- 4 , +/-6 , +/- 1/3 , +/- 2/3 , +/- 4/3
Therefore the rational roots of the given function matches the rational roots of the given equation.
Hence the correct option is A.
