Use Descartes' Rule of Signs to Determine the Total Number $$f ( x ) = 5 x ^ { 11 } + 2 x ^ { 9 } + 9 x ^ { 7 } - 9 x ^ { 6 }$$

question 129

Multiple Choice

Use Descartes' rule of signs to determine the total number of real zeros and the number of positive and
negative real zeros. (Hint: First factor out x to its lowest power.)
- $$f ( x ) = 5 x ^ { 11 } + 2 x ^ { 9 } + 9 x ^ { 7 } - 9 x ^ { 6 }$$

• A) 11 real zeros; f (x) has 1 positive real zero, 4 negative real zeros and the number 0 is a zero of multiplicity 6.
• B) 6 real zeros; f (x) has 1 positive real zero, no negative real zeros and the number 0 is a zero of multiplicity 5.
• C) 7 real zeros; f (x) has 1 positive real zero, no negative real zeros and the number 0 is a zero of multiplicity 6.
• D) 2 real zeros; f (x) has 1 positive real zero, no negative real zeros and the number 0 is a zero of multiplicity 1.

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