Use Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function. 4x⁵ - 8x A)One negative zero B)One negative zero or three positive zeros C)Two negative zeros or no positive zero D)One positive zero,one negative zero E)One negative zero,four negative zeros

Question

Quizplus · Accepted Answer

- The number of variations in sign of f(x) = 4x^3 - 8x when x is substituted with -x is: 
f(-x) = 4(-x)^3 - 8(-x) = -4x^3 + 8x 
There is only one sign change, from negative to positive. Therefore, there is only one negative root. 
- The number of variations in sign of f(x) when x is substituted with -x is: 
f(-x) = 4(-x)^3 - 8(-x) = -4x^3 + 8x 
Again, there is only one sign change, from negative to positive. Therefore, there is only one positive root. 
Therefore, there is one positive and one negative root, giving choice D as the correct answer.

Use Descartes's Rule of Signs to Determine the Possible Numbers