Question

Solve the given quadratic equation:
x² - 4x + 13 = 0

Answer 1

To solve this equation, let us apply Quadratic formula

${x}^{2} -4x + 13= 0 \\ \\ a = 1\\ \\ b = -4 \\ \\ c = 13 \\ \\ x_{1,2} = \frac{ - b ± \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x_{1,2} = \frac{ 4 ± \sqrt{ {(-4)}^{2} - 4(1)(13)} }{2 \times 1} \\ \\ x_{1,2} = \frac{ 4 ± \sqrt{ 16 - 52} }{2} \\ \\ x_{1,2} = \frac{ 4±\sqrt{ -36} }{2} \\ \\ \\ x_{1,2} = \frac{ 4 ± i6}{4} \\ \\ x_{1} = \frac{ 2 + 3i}{2} \\ \\ x_{2} = \frac{ 2 - 3i}{2}$
Hope it helps you