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OlgaM077 [116]
3 years ago
8

4

Mathematics
1 answer:
taurus [48]3 years ago
6 0

Answer:

x^2 - 2x + 10, option B

Step-by-step explanation:

Complex numbers:

The most important relation that involves complex numbers is given by:

i^2 = -1

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

In this question:

The solutions are:

x_1 = 1 - 3i, x_2 = 1 + 3i

We have to find the polynomial. All option have a = 1. So

(x - (1 - 3i))(x - (1 + 3i)) = x^2 - x(1 + 3i) - x(1 - 3i) + (1 - 3i)(1 + 3i) = x^2 - x -3ix - x + 3ix + 1^2 - (3i^2) = x^2 - 2x + 1 - 9i^2 = x^2 - 2x + 1 - 9(-1) = x^2 - 2x + 10

The correct answer is given by option b.

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