Give the maximum number of zeros the polynomial function may have. Use Descarte's Rule of Signs to determine how
many positive and how many negative zeros it may have.
-$f ( x ) = - 2 x ^ { 5 } + x ^ { 3 } - x ^ { 2 } + 3$
A) 5; 3 or 1 positive zeros; 2 or 0 negative zeros
B) 5; 2 or 0 positive zeros; 2 or 0 negative zeros
C) 5; 3 or 1 positive zeros; 3 or 1 negative zeros
D) 5; 2 or 0 positive zeros; 3 or 1 negative zeros

Question

Quizplus · Accepted Answer

The polynomial is of degree 5, so it can have a maximum of 5 zeros. Descartes' Rule of Signs shows 3 sign changes for positive zeros (3 or 1) and 2 sign changes for negative zeros (2 or 0).

Give the Maximum Number of Zeros the Polynomial Function May f(x)=−2x5+x3−x2+3f ( x ) = - 2 x ^ { 5 } + x ^ { 3 } - x ^ { 2 } + 3f(x)=−2x5+x3−x2+3

Give the Maximum Number of Zeros the Polynomial Function May $f ( x ) = - 2 x ^ { 5 } + x ^ { 3 } - x ^ { 2 } + 3$