Use Descartes' Rule of Signs and the Rational Zeros Theorem $$f ( x ) = 2 x ^ { 4 } - 12 x ^ { 3 } + 19 x ^ { 2 } - 6 x + 9$$

question 39

Multiple Choice

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the
zeros to factor f over the real numbers.
- $$f ( x ) = 2 x ^ { 4 } - 12 x ^ { 3 } + 19 x ^ { 2 } - 6 x + 9$$

• A) \(- 3,3 ; f ( x ) = ( x - 3 ) ( x + 3 ) \left( 2 x ^ { 2 } + 1 \right)\)
• B) no real roots; \(f ( x ) = \left( x ^ { 2 } + 9 \right) \left( 2 x ^ { 2 } + 1 \right)\)
• C) 3 , multiplicity \(2 ; f ( x ) = ( x - 3 ) ^ { 2 } \left( 2 x ^ { 2 } + 1 \right)\)
• D) \(- 3\), multiplicity \(2 ; f ( x ) = ( x + 3 ) ^ { 2 } \left( 2 x ^ { 2 } + 1 \right)\)

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