Question 1087618: Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function.
f(x)=x^8-12
* 0 positive zeros, 1 negative zero
* 1 positive zero, 0 negative zeros
* 1 positive zero, 1 negative zero
* 0 positive zeros, 0 negative zeros
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website! Question:
Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function.
f(x)=x^8-12
* 0 positive zeros, 1 negative zero
* 1 positive zero, 0 negative zeros
* 1 positive zero, 1 negative zero
* 0 positive zeros, 0 negative zeros
Solution:
Descartes' Rule of Signs says that the number of changes of sign of coefficients of a polynomial indicates the possible number of zeroes.
In the given case, the coefficients are +1 and -12, so one possible positive zero.
However, if we invert the sign of x, that gives the number of possible negative zeroes. The coefficients remain +1 and -12, hence there is also one possible negative zero.
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