Question

P= -5x2 + 70x - 165​

Answer 1

For this case we have the following quadratic equation:

`p = -5x ^ 2 + 70x-165`

To find the roots, we equal 0.

`-5x ^ 2 + 70x-165 = 0`

Where:

`a = -5\\b = 70\\c = -165`

The solution will be given by:

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

Substituting we have:

`x = \frac {-70 \pm \sqrt {70 ^ 2-4 (-5) (- 165)}} {2 (-5)}\\x = \frac {-70 \pm \sqrt {4900-3300}} {- 10}\\x = \frac {-70 \pm \sqrt {1600}} {- 10}\\x = \frac {-70 \pm40} {- 10}\\x = - (-7\pm4)`

We have two roots:

`x_ {1} = 7-4 = 3\\x_ {2} = 7 + 4 = 11`

Answer:

`x_ {1} = 3\\x_ {2} = 11`