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p is a degree 3 polynomial with p ( 0 ) = 22.08 and zeros 2 and 4 i . Find an equation for p with only real coefficients (i.e. no i in your equation).
Use x as your input, and round all answers to 2 decimal places as needed.

Respuesta :

mhanifa

Answer:

  • P(x) =  -0.69x³ + 2.76x² - 11.04x + 44.16

Step-by-step explanation:

Let P(x) is the function with zero's 2 and 4i.

It has to have one more zero since it is of degree 3. This is a conjugate of 4i and is -4i.

The function has the shape of:

  • P(x) = a(x - 2)(x - 4i)(x + 4i)

And we have P(0) = 22.08

Let's substitute and find the value of a:

  • 22.08 = a(0 - 2)(0 - 4i)(0 + 4i)
  • 22.08 = a(-2)(-4i)(4i)
  • 22.08 = a(-2)(-16i²)
  • 22.08 = a(-32)
  • a = - 22.08/32
  • a = - 0.69

The function is now:

P(x) = -0.69(x - 2)(x - 4i)(x + 4i)

      = -0.69(x - 4)(x² + 16)

      = -0.69(x³ - 4x² + 16x - 64)

      = -0.69x³ + 2.76x² - 11.04x + 44.16