<p>I have a trouble solving this problem.</p>
<p>Q. A polynomial function P(x) has degree n. The graph in the standard (x,y) coordinate plane of y=P(x) contains exactly 3 points on the x-axis. Which of the following could NOT be the value of n?</p>
<p>A. 6
B. 5
C. 4
D. 3
E. 2</p>
<p>Answer: E (2)</p>
<p>I don't know how you can get E for the answer... Can somebody tell me?</p>
<p>2 can't be the value of n since the function has 3 roots which implies that n is at least 3. The degree of a function determines how many roots it has, i.e. x^2 has two roots. Note that a function can have less roots than its degree, but in such a case the remaining roots are imaginary or just occur multiple times at the same place.</p>
<p>Hmmm...The number of points on the x-axis is another way to say the number of roots of the equation. </p>
<p>Any equation of degree n can cross the x-axis 0 times (the least amount of times it can cross) to "n" times (the maximum amount of times it can cross). Thus, a quadratic equation can only cross the x-axis 2 times maximum, while 3rd, 4th, 5th, and 6th degree polynomial equations can all cross the x-axis 3 or more times.</p>
<p>I can't explain why this happens, but apparently, I'm gonna learn about it in my math class.</p>
<p>Thanks tamirms and Edwardz!! I guess I have to study more...</p>