Question

Solve 3x² + 4x = 2. (2 points)

O 2 ± √10
—————
6
O −2+2√10
——————-
3
O −2+√10
——————-
3
O
-4± √10
————
3

Answer 1

Explanation:

As it is a second order equation, it means that it has two possible answers and they are
`x_1` and
`x_2`.

The famous quadratic formula for solving any second order equation is the following:

`x_(1) = (-b + √(b^2 - 4 ac))/(2a)\\x_(2)=(-b - √(b^2 - 4 ac))/(2a)`

Where a is the coefficient of
`x^2`, b is the coefficient of x, and c is the free term. In other words,

`a = 3\\b=4\\c=-2`

as the equation should be in the following form:

`a x^2 + bx+c = 0`

Therefore the possible answer should be the following,

`(-4 + √(4^2 - 4*3*(-2)))/(2*3)=(-4 +√(16 + 24))/(6) =(-4 + √(40))/(6)=\\ (-4 + √(4*10))/(6) = (-4 + 2√(10))/(6)`
`(2*(-2 + √(10)))/(2*3) = (-2 + √(10))/(3)`

by dividing the numerator and denominator by 2, we can deduce the following,