Answer:
The answer is
[tex]x = - \frac{3}{10} + \frac{ \sqrt{11} }{10} \: i \\ \\ \: OR \\ \\ x = - \frac{ 3}{10} - \frac{ \sqrt{11} }{10} \: i[/tex]
Step-by-step explanation:
5x² + 3x + 1 = 0
Using the quadratic formula
[tex]x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
From the question
a = 5 , b = 3 , c = 1
Substitute the values into the above formula and solve
That's
[tex]x = \frac{ - 3\pm \sqrt{ {3}^{2} - 4(5)(1) } }{2(5)} \\ x = \frac{ - 3\pm \sqrt{9 - 20} }{10} \\ x = \frac{ - 3\pm \sqrt{ - 11} }{10} \\ x = \frac{ - 3\pm \sqrt{11 } \: i}{10} \\ x = \frac{ - 3 + \sqrt{11} \: i}{10} \: \: or \: \: \: x = \frac{ - 3 - \sqrt{11} \: i}{10} [/tex]
Separate the real and imaginary parts
We have the final answer as
[tex]x = - \frac{3}{10} + \frac{ \sqrt{11} }{10} \: i \\ \\ x = - \frac{ 3}{10} - \frac{ \sqrt{11} }{10} \: i[/tex]
The equation has complex roots
Hope this helps you
