Question

Use the quadratic formula to solve and round to the nearest hundredth. what are the two answers? the equation is 3x squared + 13x + 5 = 0

Answer 1

For this case we have the following quadratic equation:

`3x ^ 2 + 13x + 5 = 0`

Where:

`a = 3\\b = 13\\c = 5`

Applying the quadratic formula:

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

Substituting the values:

`x = \frac {-13 \pm \sqrt {13 ^ 2-4 (3) (5)}} {2 (3)}\\x = \frac {-13 \pm \sqrt {169-60}} {6}\\x = \frac {-13 \pm \sqrt {109}} {6}`

Thus, we have two roots:

`x_ {1} = \frac {-13- \sqrt {109}} {6} = - 3.91\\x_ {2} = \frac {-13+ \sqrt {109}} {6} -0.43`

Answer:

`x_ {1} = - 3.91\\x_ {2} = - 0.43`