101k views
0 votes
What is the solution set of the equation using the quadratic formula? x2 2x 5=0

1 Answer

2 votes

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?
\(x^2 - 2x + 5 = 0\)

User Stephen Mesa
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories