College Math Placement Practice Test

Question: 1 / 400

What is the product of the roots of the equation x² - 4x + 4 = 0?

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To find the product of the roots of the quadratic equation \(x^2 - 4x + 4 = 0\), we can use Vieta's formulas, which relate the coefficients of a polynomial to sums and products of its roots.

For a quadratic equation of the form \(ax^2 + bx + c = 0\), the product of the roots (let's call them \(r_1\) and \(r_2\)) is given by the formula \(\frac{c}{a}\). In this particular equation, \(a = 1\), \(b = -4\), and \(c = 4\).

Plugging in these values into the formula for the product of the roots, we get:

\[

\text{Product of the roots} = \frac{c}{a} = \frac{4}{1} = 4.

\]

Thus, the product of the roots of the equation \(x^2 - 4x + 4 = 0\) is indeed 4.

This confirms that the correct answer is 4, validating the computations and the application of Vieta's formulas for quadratic equations.

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