Question

4

Select the equation below that has solutions of 1-3i and 1+3i *
(1 Point)
O A. O = x2 – 2x - 10
O B. 0 = x2 -- 2x + 10
O C. O = x2 – 2x + 8
O D. 0 = x2 - 2x - 8
PLS HELP!!!

Answer 1

`x^2 - 2x + 10`, option B

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\\eq0`.

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) = (-b + √(\bigtriangleup))/(2*a)`

`x_(2) = (-b - √(\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.