SOLUTION: The following table gives some of the values of a 5th degree polynomial p(x). Based on the values shown, what is the minimum number of real roots of the equation p(x) = 0? The

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Question 45992: The following table gives some of the values of a 5th degree polynomial p(x).
Based on the values shown, what is the minimum number of real roots of the equation p(x) = 0?
The Table
x 0, 1, 2, 3, 4, 5, 6, 7
p(x) -30, 22, 110, 150, 34, -130, 222, 2,350
The choices for answers are
(A) one
(B) two
(C) three
(D) four
(E) five
The answer is (C) three real roots
I don't understand how they got this answer. Thank you for your help.
Cindy Konopasek
Answer by Nate(3500) (Show Source):
You can put this solution on YOUR website!
Real roots are the zero points(where the line travels through the x-axis). For the line to travel through the x-axis, the values must go from positive to negative or from negative to postive.
< for negative and > for positive
p(x) -30 <, 22 >, 110 >, 150 >, 34 >, -130 <, 222 >, 2,350 >
One Root: from NEGATIVE thirty - to - POSITIVE 22
Second Root: from POSITIVE thirty four - to - NEGATIVE 130
Third Root: from NEGATIVE -130 - to - POSITIVE 222