Find a Quadratic Equation with Rational Coefficients, One of Whose $x ^ { 2 }$

question 4

Multiple Choice

Find a quadratic equation with rational coefficients, one of whose roots is the given number. Write your answer so that the coefficient of
$x ^ { 2 }$ is 1. $r _ { 1 } = 1 + \sqrt { 2 }$

• A) \(x ^ { 2 } - 3 x - 1 = 0\)
• B) \(x ^ { 2 } - 2 x - 8 = 0\)
• C) \(x ^ { 2 } - 2 x - 1 = 0\)
• D) \(x ^ { 2 } - 2 x - 9 = 0\)
• E) \(x ^ { 2 } - 2 x - 3 = 0\)

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Definitions:

F-distributed

Pertaining to an F-distribution, used in statistical analysis to compare variances.

Independent Samples

Two or more groups of observations that are collected from different populations and have no relationship with each other.

Population Variances

A measure of the dispersion or spread of a set of data points in a population, indicating how much the data points differ from the population mean.

Independent Samples

Samples that are collected without any natural pairing or linkage between the observations in each sample.