Use Descartes's Rule of Signs to determine the possible numbers of positive and neg- ative zeros of the function. $6 x ^ { 5 } - 12 x$
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

Descartes's Rule of Signs states that the number of positive real zeros is equal to the number of sign changes in the polynomial or less than that by an even number. For $6x^5 - 12x$, there is one sign change, indicating one positive zero. For negative zeros, substitute $x$ with $-x$ to get $-6x^5 - 12x$, which has one sign change, indicating one negative zero.

Use Descartes's Rule of Signs to Determine the Possible Numbers 6x5−12x6 x ^ { 5 } - 12 x6x5−12x

Use Descartes's Rule of Signs to Determine the Possible Numbers $6 x ^ { 5 } - 12 x$