Steven G
Elite Member
- Joined
- Dec 30, 2014
- Messages
- 14,596
I am helping a neighbor prepare for the SAT Math Subject test and came upon this problem.
If f(x) = x^4 -3x^3 -9x^2 + 4, for how many real numbers k does f(k) = 2
The choices are 0, 1, 2, 3 or 4
Of course 1 and 3 are ruled out. The only method I could thing of after trying the rational root test was to try using the IVT. I did not bother with Descartes' rule of signs as it is a timed exam and I felt it would be too time consuming. I tested the first few positive and negative numbers and found 3 sign changes and concluded there were four values for k.
My concern is that a student taking the SAT Subject test should not know the IVT (although they should figure that rule on their own)
Any quicker methods for this problem (other than using technology)?
If f(x) = x^4 -3x^3 -9x^2 + 4, for how many real numbers k does f(k) = 2
The choices are 0, 1, 2, 3 or 4
Of course 1 and 3 are ruled out. The only method I could thing of after trying the rational root test was to try using the IVT. I did not bother with Descartes' rule of signs as it is a timed exam and I felt it would be too time consuming. I tested the first few positive and negative numbers and found 3 sign changes and concluded there were four values for k.
My concern is that a student taking the SAT Subject test should not know the IVT (although they should figure that rule on their own)
Any quicker methods for this problem (other than using technology)?