Question

Solve the quadratic equation.

x^2 - 2x + 6 = 0

answers below:

x = 2 ± square root 20

x = 2 ± square root 28

x = - 2 ± square root 28

no real solution

Answer 1

To solve the quadratic equation \(x^2 - 2x + 6 = 0\), we can use the quadratic formula:

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

where \(a = 1\), \(b = -2\), and \(c = 6\).

First, we calculate the discriminant (\(b^2 - 4ac\)):

\[
b^2 - 4ac = (-2)^2 - 4(1)(6) = 4 - 24 = -20
\]

Since the discriminant is negative (\(-20\)), this implies that there are no real solutions for the equation \(x^2 - 2x + 6 = 0\).

Thus, the correct answer is:

**no real solution**.