Question

What are the solutions of 3x^2 + 14x + 16 = 0?

x = -8/3, –2

x = –2, -3/8

x = 3/8, 2

x = 8/3, 2

Answer 1

the solution is :
x= -8/3 , -2

Answer 2

The correct option is A) x = -8/3, –2.

Explanation:

Consider the provided equation
`3x^2 + 14x + 16 = 0`

The above equation is in the form of
`ax^2 +bx + c = 0`

The quadratic formula to find the root of the equation is:

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

By comparing the above equation with the general equation we can conclude that:

a = 3, b = 14, and c = 16

Substitute the respective values in the above formula:

`{\displaystyle x={\frac {-14\pm {\sqrt {14^(2)-4(3)(16)}}}{2(3)}}\ \ }`

`{\displaystyle x={\frac {-14\pm {\sqrt {196-192}}}{6}}\ \ }`

`{\displaystyle x={\frac {-14\pm {\sqrt {4}}}{6}}\ \ }`

`{\displaystyle x={\frac {-14\pm2}{6}}\ \ }`

`{\displaystyle x={\frac {-14+2}{6}}\ \ } or\ {\displaystyle x={\frac {-14-2}{6}}\ \ }`

`{\displaystyle x={\frac {-12}{6}}\ \ } or\ {\displaystyle x={\frac {-16}{6}}\ \ }`

`{\displaystyle x=-2}\ \ } or\ {\displaystyle x={\frac {-8}{3}}\ \ }`

Hence the solutions of the provided equation is
`{\displaystyle x=-2}\ \ } or\ {\displaystyle x={\frac {-8}{3}}\ \ }`.

Thus, the correct option is A) x = -8/3, –2.