Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given
function.
-$$f ( x ) = - 7 x ^ { 9 } + x ^ { 7 } - x ^ { 2 } + 3$$
A) 3 or 1 positive zeros, 2 or 0 negative zeros
B) 3 or 1 positive zeros, 3 or 1 negative zeros
C) 2 or 0 positive zeros, 2 or 0 negative zeros
D) 2 or 0 positive zeros, 3 or 1 negative zeros

Question

Quizplus · Accepted Answer

Descartes's Rule of Signs indicates 3 or 1 positive zeros due to 3 sign changes in $f(x)$, and 2 or 0 negative zeros due to 2 sign changes in $f(-x)$.

Use Descartes's Rule of Signs to Determine the Possible Number f(x)=−7x9+x7−x2+3f ( x ) = - 7 x ^ { 9 } + x ^ { 7 } - x ^ { 2 } + 3f(x)=−7x9+x7−x2+3

Use Descartes's Rule of Signs to Determine the Possible Number $f ( x ) = - 7 x ^ { 9 } + x ^ { 7 } - x ^ { 2 } + 3$