Solve by using the quadratic formula. Put answer in exact value, simplest radical form. 3x^2 + 6x + 2 = 0

2 Answers

baxthum8's profile pic

baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted on

`3x^2 + 6x + 2 = 0` This equation is written in `ax^2 + bx + c` form.

Therefore, `a = 3, b = 6, and c = 2`

The quadratic formula is:  `(-b+-sqrt(b^2 - 4ac))/(2a)`

Substituting 3, 6, and 2 for a, b, and c respectively we get:

`( -6+-sqrt(6^2-4*3*2)) / ( 2*3 )`

Simplyfing in radical we get:  `( -6+-sqrt(12)) / 6`

`sqrt(12)` can be simplified: `sqrt(12) =sqrt(4)*sqrt(3)` `rArr` `2sqrt(3)`

Now we have:  `( -6+-2sqrt(3)) / 6`

Since all terms have a common factor of 2, we will simplify and get:

`( -3+-sqrt(3) ) / 3`