Question

Use the quadratic formula to find both solutions to the quadratic equation given below 3x^2-x+5=0

Answer 1

For this case we have the following quadratic equation:

`3x ^ 2-x + 5 = 0`

We have to:

`a = 3\\b = -1\\c = 5`

The quadratic equation states that:

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

Substituting the values we have:

`x = \frac {- (- 1) \pm \sqrt {(- 1) ^ 2-4 (3) (5)}} {2 (3)}\\x = \frac {1 \pm \sqrt {1-60}} {6}\\x = \frac {1 \pm \sqrt {-59}} {6}\\x = \frac {1 \pm \sqrt {59i ^ 2}} {6}\\x = \frac {1 \pm i \sqrt {59}} {6}`

We have two roots:

`x_ {1} = \frac {1 + i \sqrt {59}} {6}\\x_ {2} = \frac {1-i \sqrt {59}} {6}`

Answer:

`x_ {1} = \frac {1 + i \sqrt {59}} {6}\\x_ {2} = \frac {1-i  \sqrt {59}} {6}`