• Jun 30th 2009, 01:19 PM
MR FRESH
Choose the statement that is true about the given quantities.

Selection A:
The number of rational zeros of f(x)=x^3 + 2x^2 - 11x -12.

Selection B:
The number of rational zeros of f(x)=x^3 - 8x^2 +16x +25.

A)The two quantities are equal.
B)The quantity in Selection A is greater.
C)The quantity in Selection B is greater.
D)The relationship cannot be determined from the given information
• Jun 30th 2009, 01:28 PM
VonNemo19
Quote:

Originally Posted by MR FRESH
Choose the statement that is true about the given quantities.

Selection A:
The number of rational zeros of f(x)=x^3 + 2x^2 - 11x -12.

Selection B:
The number of rational zeros of f(x)=x^3 - 8x^2 +16x +25.

A)The two quantities are equal.
B)The quantity in Selection A is greater.
C)The quantity in Selection B is greater.
D)The relationship cannot be determined from the given information

To test if a is true set the two equal to each other and see what happens. This will also tell you which one's greater.
• Jun 30th 2009, 03:16 PM
HallsofIvy
By the "rational root theorem", any rational root of $a_nx^n+ a_{n-1}x^{n-1}+ \cdot\cdot\cdot+ a_1x+ a_0= 0$, m/n, must have m a divisor of $a_0$ and n a divisor of $a_n$.

In the first equation, $a_n= a_3= 1$ and $a_0= -12$ so any rational root must divide -12. What are the divisors of -12? How many of them actually satisfy the equation?

In the second equation, $a_n= a_3= 1$ and $a_0= 25$ so any rational root must divide 25. What are the divisors of 25? How many of them actually satisfy the equation?