Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function.
-$$2 x ^ { 6 } - 3 x ^ { 4 } - 8 x ^ { 3 } + 6 x ^ { 2 } - 3 x = 0$$
A) Positive $( 2,0 )$, negative $( 3,1 )$
B) Positive $( 3,1 )$, negative $( 2,0 )$
C) Positive $( 3,1 )$, negative (2)
D) Positive $( 2,0 )$, negative $( 0 )$

Question

Quizplus · Accepted Answer

The function has 3 sign changes for positive zeros and 2 sign changes for negative zeros, leading to possibilities of (3,1) for positive and (2,0) for negative zeros.

Use Descartesʹ Rule of Signs to Determine the Possible Number 2x6−3x4−8x3+6x2−3x=02 x ^ { 6 } - 3 x ^ { 4 } - 8 x ^ { 3 } + 6 x ^ { 2 } - 3 x = 02x6−3x4−8x3+6x2−3x=0

Use Descartesʹ Rule of Signs to Determine the Possible Number $2 x ^ { 6 } - 3 x ^ { 4 } - 8 x ^ { 3 } + 6 x ^ { 2 } - 3 x = 0$