Question

What is the solution set of the equation using the quadratic formula? x2 2x 5=0

Answer 1

The solution set for the quadratic equation
`\(x^2 - 2x + 5 = 0\) is \(\{1 + 2i, 1 - 2i\}\)`.

The given quadratic equation is
`\(x^2 - 2x + 5 = 0\)`, and we have found the solutions using the quadratic formula:

`\[ x = (-b \pm √(b^2 - 4ac))/(2a) \]`

In this case,
`\(a = 1\), \(b = -2\), and \(c = 5\)`. Substitute these values into the formula:

`\[ x = (-(-2) \pm √((-2)^2 - 4(1)(5)))/(2(1)) \]`

Simplify further:

`\[ x = (2 \pm √(4 - 20))/(2) \]`

`\[ x = (2 \pm √(-16))/(2) \]`

Since the square root of -16 is an imaginary number
`(\(√(-16) = 4i\))`, we have two complex conjugate solutions:

`\[ x_1 = (2 + 4i)/(2) = 1 + 2i \]`

`\[ x_2 = (2 - 4i)/(2) = 1 - 2i \]`

Complete the question:

What is the solution set of the equation using the quadratic formula?
`\(x^2 - 2x + 5 = 0\)`