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by shashank.ism » Fri Feb 05, 2010 10:57 pm
P(x) is a third degree polynomial and the coefficients of P(x) are rational. If the graph of P(x) touches the x-axis, then how many rational roots does P(x) = 0 have?
a.) 2
b.) 0
c.) 1
d.) 3
e.) none of these
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by Brent@GMATPrepNow » Fri Feb 05, 2010 11:16 pm
shashank.ism wrote:P(x) is a third degree polynomial and the coefficients of P(x) are rational. If the graph of P(x) touches the x-axis, then how many rational roots does P(x) = 0 have?
a.) 2
b.) 0
c.) 1
d.) 3
e.) none of these
The wording makes this questions wayyyy out of scope. You do not need to be familiar with terms such as "third degree" and "coefficients."
Aside: I also think this is a bad question (unless "touches" is meant to imply that there are two identical roots at one point, and "how many roots" implies "how many unique roots").
If this is not what is meant by "touches" then there is more than one correct answer.
For example, we could have 1 unique root as in P(x) = x^3 (x=0)
We could have 3 unique roots as in P(x) = x^3 - 4x (x=-2, 2, 0)
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