Question

Find the solutions of the quadratic equation 5x^2 +3x+1=0

Answer 1

Answer:

The answer is

$x = - \frac{3}{10} + \frac{ \sqrt{11} }{10} \: i \\ \\ \: OR \\ \\ x = - \frac{ 3}{10} - \frac{ \sqrt{11} }{10} \: i$

Step-by-step explanation:

5x² + 3x + 1 = 0

Using the quadratic formula

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

From the question

a = 5 , b = 3 , c = 1

Substitute the values into the above formula and solve

That's

$x = \frac{ - 3\pm \sqrt{ {3}^{2} - 4(5)(1) } }{2(5)} \\ x = \frac{ - 3\pm \sqrt{9 - 20} }{10} \\ x = \frac{ - 3\pm \sqrt{ - 11} }{10} \\ x = \frac{ - 3\pm \sqrt{11 } \: i}{10} \\ x = \frac{ - 3 + \sqrt{11} \: i}{10} \: \: or \: \: \: x = \frac{ - 3 - \sqrt{11} \: i}{10}$

Separate the real and imaginary parts

We have the final answer as

$x = - \frac{3}{10} + \frac{ \sqrt{11} }{10} \: i \\ \\ x = - \frac{ 3}{10} - \frac{ \sqrt{11} }{10} \: i$

The equation has complex roots

Hope this helps you