Question

Roots of -2x^2 -6x+5=0

Answer 1

For this case we have the following quadratic equation:

`-2x ^ 2 -6x + 5 = 0`

Where:

`a = -2\\b = -6\\c = 5`

The roots will be given by the following formula:

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

Substituting the values we have:

`x = \frac {- (- 6) \pm \sqrt {(- 6) ^ 2-4 (-2) (5)}} {2 (-2)}\\x = \frac {6 \pm \sqrt {36 + 40}} {- 4}\\x = \frac {6 \pm \sqrt {76}} {- 4}\\x = \frac {6 \pm \sqrt {2 ^ 2 * 19}} {- 4}\\x = \frac {6 \pm2 \sqrt {19}} {- 4}\\x = \frac {3 \pm \sqrt {19}} {- 2}`

We have two roots:

`x_ {1} = \frac {-3- \sqrt {19}} {-2}\\x_ {2} = \frac {-3+ \sqrt {19}} {2}`

Answer:

`x_ {1} = \frac {-3- \sqrt {19}} {2}\\x_ {2} = \frac {-3+ \sqrt {19}} {2}`