bellwork perform the operation and write the result in standard from ( a + bi)
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2.5 Real and Complex Zeros of Polynomial Functions -How to find all zeros of polynomial functions, including complex zeros?TRANSCRIPT
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Bellwork
iii
ii
32)5)(32()2
24)1 2
Perform the operation and write the result in standard from ( a + bi)
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Last Nights Homework• 15. 11-i• 17. 7 - 3√2 i• 20. 17 + 18i• 30. 6 – 22i• 31. 12 + 30i• 34. 21-3√10 i + 7√5 i + √50• 47. -6i• 49. (16 + 20i)41• 59. -1 + 6i• 66. -1/8• 11-14. Will graph
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2.5 Real and Complex Zeros of Polynomial Functions-How to find all zeros of polynomial functions, including complex zeros?
![Page 4: Bellwork Perform the operation and write the result in standard from ( a + bi)](https://reader036.vdocuments.net/reader036/viewer/2022082621/5a4d1b527f8b9ab0599a81f8/html5/thumbnails/4.jpg)
Every nth degree polynomial has precisely n zeros.
96)()
2)()
2
xxxfb
xxfa
Example 1: Find all the real and complex roots.
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Example 1: Find all roots, complex and real. xxxfc 4)() 3 1)() 4 xxfd
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Example 2: Find all zeros, real and complex.
16124)() 23 xxxxfa Start by finding zeroes in the calculator, use synthetic division, and then quadratic formula for the rest.
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Example 2: Find all zeros, real and complex.
1812113)() 23 xxxxfb Start by finding zeroes in the calculator, use synthetic division, and then quadratic formula for the rest.
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Complex zeros occur in conjugate pairs.
• Let f(x) be a polynomial function that has real coefficients. If a + bi, where b is not 0, is a zero of the function, the conjugate a – bi is also a zero of the function.
)3)(3)(1)(1()( ixixxxxf
918102)( 234 xxxxxf
Example 3: Find a fourth degree polynomial function, with real coefficients, that has -1, -1 and 3i as zeros.
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Tonight’s Homework• Pg 187 #17, 19, 29, 38(just find all zeroes), 41, 43, 45, 65