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egoroff_w [7]
3 years ago
6

one edition of alice's adventures in wonderland has 352 pages. How many 4s were used in its page numbers

Mathematics
1 answer:
Tema [17]3 years ago
7 0
35 4's were used when writing this book
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Step-by-step explanation:

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Given 1+2i as a zero of f(x) = x^4 - 2x^3 - 4x^2 + 18x - 45, find all other zeros and write the complete factorization. Please s
tatuchka [14]

Answer:

  • (x + 3)(x - 3)(x² - 2x + 5)

Step-by-step explanation:

<u>One of the zeros given:</u>

  • 1 + 2i

<u>Since it is a complex number, its conjugate is also a zero:</u>

  • 1 - 2i

<u>The product of two factors are:</u>

  • (x - (1 + 2i))(x - (1 - 2i)) =
  • x² - x(1 + 2i + 1 - 2i) + (1 - 4i²) =
  • x² - 2x + 5

<u>We need two more zeros. Let them be m and n, then we have:</u>

  • (x - m)(x - n) = x² - (m +n)x + mn

<u>The product of all factors:</u>

  • (x² - 2x + 5)(x² - (m+n)x + mn) = x⁴ - 2x³ - 4x² + 18x - 45
  • x⁴- (m+n+2)x³ + (mn+5)x² - (2mn+5m+5n)x + 5mn = x⁴- 2x³- 4x²+ 18x- 45

<u>Compare left and right sides and solve for m and n:</u>

  • m + n + 2 = 2 ⇒ m + n = 0
  • mn + 5 = -4 ⇒ mn = -9
  • 2mn + 5(m + n) = -18 ⇒ mn = -9

<u>From the above equations we get:</u>

  • m = -n
  • -n² = -9
  • n = 3
  • m = -3

The other zero's are 3 and -3

<u>All of the factors:</u>

  • (x + 3)(x - 3)(x² - 2x + 5)
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3 years ago
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