Question

Use the quadratic formula to find the solutions to the equation.

x2 – 3x + 1 = 0

Answer 1

To solve the quadratic equation \( x^2 - 3x + 1 = 0 \) using the quadratic formula, we can use the formula:

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

In this equation, the coefficients are:
- \( a = 1 \)
- \( b = -3 \)
- \( c = 1 \)

Now, we can substitute these values into the quadratic formula.

1. Calculate the discriminant (\( b^2 - 4ac \)):

\[
b^2 - 4ac = (-3)^2 - 4(1)(1) = 9 - 4 = 5
\]

2. Now substitute these values into the quadratic formula:

\[
x = \frac{-(-3) \pm \sqrt{5}}{2(1)} = \frac{3 \pm \sqrt{5}}{2}
\]

Thus, the two solutions to the equation \( x^2 - 3x + 1 = 0 \) are:

\[
x = \frac{3 + \sqrt{5}}{2} \quad \text{and} \quad x = \frac{3 - \sqrt{5}}{2}
\]