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write a polynomial function if its leading coefficient is -3, and its roots include 4, 0 and 5x-2i.

Sagot :

mhanifa

Answer:

  • See below

Step-by-step explanation:

Given a polynomial with:

  • The leading coefficient is - 3
  • Roots are 4, 0, 5 - 2i

We know the complex roots should be paired with their conjugate.

So 5 + 2i is also a root.

The least polynomial is:

f(x) = - 3(x - 4)(x - 0)(x - 5 - 2i)(x - 5 + 2i) =

         -3x(x - 4)(x² - 10x + 29) =

         -3x(x³ - 14x² + 69x - 116) =

         -3x⁴ + 42x³ - 207x² + 348x

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