Question

Select the two values of x that are roots of this equation.
x2-5x +2=0
• ×=
5+v/33
2
Х =
5-v17
2
•x=
5-33
2
•x=
5+v17
2

Answer 1

To find the roots of the quadratic equation \(x^2 - 5x + 2 = 0\), we can use the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

In our equation, the coefficients are:
- \(a = 1\)
- \(b = -5\)
- \(c = 2\)

Now, substituting these values into the formula:

1. Calculate the discriminant:
\[
b^2 - 4ac = (-5)^2 - 4 \cdot 1 \cdot 2 = 25 - 8 = 17
\]

2. Now substitute into the quadratic formula:
\[
x = \frac{5 \pm \sqrt{17}}{2}
\]

From this, we have two roots:
1. \(x = \frac{5 + \sqrt{17}}{2}\)
2. \(x = \frac{5 - \sqrt{17}}{2}\)

Now, we can match these with the presented options:

- \(x = \frac{5 + \sqrt{33}}{2}\) (Incorrect)
- \(x = \frac{5 - \sqrt{17}}{2}\) (Correct)
- \(x = \frac{5 - 33}{2}\) (Incorrect)
- \(x = \frac{5 + \sqrt{17}}{2}\) (Correct)

Thus, the two values of \(x\) that are roots of the equation \(x^2 - 5x + 2 = 0\) are:

- \(x = \frac{5 + \sqrt{17}}{2}\)
- \(x = \frac{5 - \sqrt{17}}{2}\)