Question

What are the solutions of 4x2-x+9=0

Answer 1

For this case we must find the solutions of the following equation:

`4x ^ 2-x + 9 = 0`

We apply the cudratic formula:

`x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}`

Where:

`a = 4\\b = -1\\c = 9`

Substituting:

`x = \frac {- (- 1) \pm \sqrt {(- 1) ^ 2-4 (4) (9)}} {2 (4)}\\x = \frac {1 \pm \sqrt {1-144}} {8}\\x = \frac {1 \pm \sqrt {-143}} {8}`

Thus, the complex roots are:

`x_ {1} = \frac {1 + i \sqrt {143}} {8}\\x_ {2} = \frac {1-i \sqrt {143}} {8}`

Answer:

`x_ {1} = \frac {1 + i \sqrt {143}} {8}\\x_ {2} = \frac {1-i \sqrt {143}} {8}`