Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given
function.
-$$f ( x ) = x ^ { 7 } + x ^ { 6 } + x ^ { 2 } + x + 10$$
A) 0 positive zeros, 3 or 1 negative zeros
B) 0 positive zeros, 0 negative zeros
C) 0 positive zeros, 2 or 0 negative zeros
D) 0 positive zeros, 1 negative zero

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 coefficients of the function when written in standard form, or the number of sign changes minus an even number. The number of negative real zeros is equal to the number of sign changes in the coefficients of the function when written in standard form, or the number of sign changes minus an odd number.For the given function, there are no sign changes in the coefficients when written in standard form, so there are 0 positive real zeros. There is 1 sign change in the coefficients when written in standard form, so there are 1 or 3 negative real zeros.

Use Descartes's Rule of Signs to Determine the Possible Number f(x)=x7+x6+x2+x+10f ( x ) = x ^ { 7 } + x ^ { 6 } + x ^ { 2 } + x + 10f(x)=x7+x6+x2+x+10

Use Descartes's Rule of Signs to Determine the Possible Number $f ( x ) = x ^ { 7 } + x ^ { 6 } + x ^ { 2 } + x + 10$