Monday, February 8, 2010

Which one of these math statements is false?

Let P(x) be a fourth-degree polynomial with real coefficients. Indicate


which of the following statements is FALSE. (There is only one correct


answer).





A. P(x) has exactly four zeros.


B. If we know P(x) has three real zeros, then the fourth zero must be


real.


C. P(x) has at least two real zeros.


D. If P(x) -%26gt; infinity as x -%26gt; infinity , then it must be true that P(x) -%26gt; infinity as x -%26gt; negative infinityWhich one of these math statements is false?
C.





An example is X^4 + X^3 + X^2 + X + 100


No real 0s on that graphWhich one of these math statements is false?
C is the correct response.





Consider the equation P(x)=x^4 + 1





This equation never crosses the x axis, and has no real zeros. BUT, it does have four non-real zeros.





A is TRUE because a polynomial with real coefficients has the same number of roots as its degree. (By the rational root theorem)





B is TRUE because all non-real zeros come in pairs (see the fundamental theorem of algebra; the rational root theorem)





D is TRUE because of the behavior of the even functions.





I hope this helped!
A is false. P(x) could have the same zero twice and not have four unique zeros.


B is true. Imaginary zeros come in pairs. You can't have just 1.


Since B is true, C and D must be false.
This is a guess!!!


B. If we know P(x) has three real zeros, then the fourth zero must be


real.

No comments:

Post a Comment