Question

Solve 3x^2 +11x+6=0

Answers

-2/3,-3

2/3,3

0

Answer 1

Answer: First Option

`x_1=-(2)/(3)` and
`x_2=-3`

Explanation:

We have the following quadratic equation:

`3x^2 +11x+6=0`

To solve this equation use the quadratic formula

For an equation of the form:

`ax ^ 2 + bx + c = 0`

The quadratic formula is:

`x=(-b\±√(b^2-4ac))/(2a)`

Note that in this case:
`a=3,\ b=11,\ c=6`

Then:

`x=(-11\±√(11^2-4(3)(6)))/(2(3))`

`x=(-11\±√(121-72))/(6)`

`x=(-11\±√(49))/(6)`

`x=(-11\±7)/(6)`

`x_1=(-11+7)/(6)`

`x_1=-(2)/(3)`

`x_2=(-11-7)/(6)`

`x_2=(-18)/(6)`

`x_2=-3`

The solutions are:
`x_1=-(2)/(3)` and
`x_2=-3`

Answer 2

-
`(2)/(3)`,-3

Explanation:

Given equation,

`3x^2+11x+6=0`

By the middle term splitting,

`3x^2 + (9+2)x + 6 = 0`

`3x^2 + 9x + 2x + 6 = 0`

`3x(x+3)+2(x+3)=0`

`(3x+2)(x+3)=0`

By zero product product,

3x + 2 = 0 or x + 3 = 0

x =
`-(2)/(3)` or x = -3

which is the solution of the given equation.

Hence, FIRST option is correct.