What is the product of the roots of the equation x^2 - 4x + 3 = 0?

What is the product of the roots of the equation x^2 - 4x + 3 = 0?

• A. 1
• B. 2
• C. 3
• D. 4

Answer: (C)

To determine the product of the roots of the quadratic equation \(x^2 - 4x + 3 = 0\), we can use Vieta's formulas. According to Vieta's formulas, for a quadratic equation of the standard form \(ax^2 + bx + c = 0\), the product of the roots is given by \(\frac{c}{a}\). In this case, the coefficients are: - \(a = 1\) - \(b = -4\) - \(c = 3\) Using the formula, the product of the roots is: \[ \text{Product of the roots} = \frac{c}{a} = \frac{3}{1} = 3 \] Thus, the product of the roots of the given equation is indeed 3, confirming that the correct answer is 3. This aligns with the option provided, which is why it is the right choice. Other calculations such as finding the roots directly using the quadratic formula or factoring could also provide the same result, but Vieta's relations give a quick and efficient method to find the product of the roots directly from the equation's coefficients.

To determine the product of the roots of the quadratic equation (x^2 - 4x + 3 = 0), we can use Vieta's formulas. According to Vieta's formulas, for a quadratic equation of the standard form (ax^2 + bx + c = 0), the product of the roots is given by (\frac{c}{a}).

In this case, the coefficients are:

• (a = 1)

• (b = -4)

• (c = 3)

Using the formula, the product of the roots is:

[

\text{Product of the roots} = \frac{c}{a} = \frac{3}{1} = 3

]

Thus, the product of the roots of the given equation is indeed 3, confirming that the correct answer is 3. This aligns with the option provided, which is why it is the right choice. Other calculations such as finding the roots directly using the quadratic formula or factoring could also provide the same result, but Vieta's relations give a quick and efficient method to find the product of the roots directly from the equation's coefficients.