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2 years ago

Write a polynomial function of the least degree that has roots of 3 and (4 + i).

Mathematics

1 answer:

polet [3.4K]2 years ago

4 0

Answer:

x³ - 11x² + 41x - 51

Step-by-step explanation:

The least number of degree is 3 and the third root should be (4 - i) to make polynomial rational.

<u>The polynomial is:</u>

(x - 3)(x - (4 + i))(x - (4 + i)) =
(x - 3)(x² -x(4 + i + 4 - i) + (4 + i)(4 - i)) =
(x - 3)(x² - 8x + 16 - (-1)) =
(x - 3)(x² - 8x + 17) =
x³ - 8x² + 17x - 3x² + 24x - 51 =
x³ - 11x² + 41x - 51

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Recall that,

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and

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$P(B \: and \: C) = P(B) \times P(C)$
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We multiply out to get,

$P(B \: and \: C) = \frac{1}{6}$

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