* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download PRECALCULUS HONORS TEST REVIEW 2.5 Find all the zeros of
Survey
Document related concepts
Big O notation wikipedia , lookup
Vincent's theorem wikipedia , lookup
Function (mathematics) wikipedia , lookup
History of the function concept wikipedia , lookup
Dirac delta function wikipedia , lookup
System of polynomial equations wikipedia , lookup
Non-standard calculus wikipedia , lookup
Elementary mathematics wikipedia , lookup
Factorization wikipedia , lookup
Division by zero wikipedia , lookup
Fundamental theorem of algebra wikipedia , lookup
Transcript
PRECALCULUS HONORS TEST REVIEW 2.5 Find all the zeros of the function. 1. f (x) = 3x(x − 2)2 2. f (x) = x 3 + 6x 3. f (x) = (x − 8)(x − 5)2 (x − 3 + i)(x − 3 − i) Use the Rational Zero Test to list all possible rational zeros of f. 4. f (x) = −4 x 3 + 8x 2 − 3x + 15 Find all rational zeros of the function. 5. f (x) = x 3 − 2x 2 − 21x − 18 6. f (x) = 25x 4 + 25x 3 − 154 x 2 − 4 x + 24 Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) 7. 2 , 4, i 3 3 Use the given zero to find all the zeros of the function. 8. f (x) = x 3 − 4 x 2 + x − 4 9. f (x) = 2x 4 − 3x 3 − 13x 2 + 37x − 15 zero : i zero : 2 + i Find all the zeros of the functions and write the polynomial as a product of linear factors. 10. f (x) = x 4 + 8x 3 + 8x 2 − 72x − 153 11. f ( x) = 3 x 3 − 20 x 2 + 7 x + 30 Use Descartes’s Rule of Signs to determine the possible numbers of positive and negative zeros of the function. 12. g(x) = 5x 3 + 3x 2 − 6x + 9 Use synthetic division to verify the upper and lower bounds of the real zeros of f. f (x) = 4 x 3 − 3x 2 + 4 x − 3 13. (a) Upper: (b) Lower: x =1 x=− 1 4