POLYNOMIAL PROBLEMS+

# POLYNOMIAL PROBLEMS+ - AP CALCULUS POLYNOMIAL SUPPLEMENTARY...

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AP CALCULUS POLYNOMIAL SUPPLEMENTARY Problems : 1) If () x 1 2 is a factor of 12 31 14 432 x x x ax b −+ + + , then a) find the values of a and b . b) find the other two factors. 2) Consider the function fx x x =−+ 16 16 1 42 for the following questions. a) Show that there are no rational roots to ( ) . b) Prove that there are roots within the following intervals: 1 2 0 , , 0 1 2 , and 1 2 1 , . State any necessary theorems in your proof. c) How many real roots does have? Explain your reasoning. d) Using the substitution u x = 2 , find the exact value of all the roots of ( ) . e) The roots of can be expressed was x = cos α , x = cos β , x = cos γ and x = cos θ where [] 0 360 , o , 0360 , o , , o and , o . Find the values of , , and . f) Prove the trigonometric identity: ( )( )( ) cos cos cos cos 15 75 105 165 1 16 oo o o = . Hint : Use will need to use the standard and factored forms of ( ) . g) Find the range of . Hint : The range of is dependent on the absolute minimum of the function. Since resembles something like a quadratic, you should try completing the square.

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## This note was uploaded on 07/27/2010 for the course MATH MATH 1025 taught by Professor Tanny during the Spring '09 term at York University.

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POLYNOMIAL PROBLEMS+ - AP CALCULUS POLYNOMIAL SUPPLEMENTARY...

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