Question

Solve x2−2x+5=0 (1 point) Responses −1, −5 −1, −5 1±i 1±i 1±2i 1 plus or minus 2 i No solution

Answer 1

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

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

In our equation, \(a = 1\), \(b = -2\), and \(c = 5\). Substituting these values into the formula gives:

\[
x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4 \cdot 1 \cdot 5}}{2 \cdot 1}
\]
\[
x = \frac{2 \pm \sqrt{4 - 20}}{2}
\]
\[
x = \frac{2 \pm \sqrt{-16}}{2}
\]
\[
x = \frac{2 \pm 4i}{2}
\]
\[
x = 1 \pm 2i
\]

Thus, the solutions are:

\[
x = 1 + 2i \quad \text{and} \quad x = 1 - 2i
\]

So the correct response is \(1 \pm 2i\).