Need on these two cause i’m very lost on them

Comments (3) on “Need on these two cause i’m very lost on them”

1. Dis the correct answer

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2. 215.92 dollars is the answer

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3. see explanation

   Step-by-step explanation:

   Given

   f(x) = (x - 4)(2x - 1)²(x - 2)²

   To find the roots equate f(x) to zero, that is

   (x - 4)(2x- 1)²(x - 2)² = 0

   Equate each of the factors to zero and solve for x

   x - 4 = 0 ⇒ x = 4

   2x - 1 = 0 ⇒ x = [tex]\frac{1}{2}[/tex]  ← with multiplicity 2

   x - 2 = 0 ⇒ x = 2 ← with multiplicity 2

   Hence the roots are

   { 4, [tex]\frac{1}{2}[/tex], 2 }

   Given

   f(x) = x³ + 4x² + 7x + 6

   Note that

   f(- 2) = (- 2)³ + 4(- 2)² + 7(- 2) + 6 = - 8 + 16 - 14 + 6 = 0

   Since f(- 2) = 0 then by the factor theorem x = - 2 is a root and (x + 2) a factor

   Using synthetic division

   - 2 | 1   4    7    6

            - 2  - 4  - 6

   --------------

        1    2    3    0

   Thus

   f(x) = (x + 2)(x² + 2x + 3)

   Solve x² + 2x + 3 using the quadratic formula

   with a = 1, b = 2 and c = 3

   x = (- 2 ± [tex]\sqrt{2^2-(4(1)(3)}[/tex] ) / 2

     = ( - 2 ± [tex]\sqrt{4-12}[/tex] ) / 2

     = ( - 2 ± [tex]\sqrt{-8}[/tex] ) / 2

     = (- 2 ± 2i[tex]\sqrt{2}[/tex] ) / 2

     = - 1 ± i[tex]\sqrt{2}[/tex]

   Hence roots are

   { - 2, - 1 + i[tex]\sqrt{2}[/tex], - 1 - i[tex]\sqrt{2}[/tex] }

        

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