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ryzh [129]
2 years ago
12

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

Mathematics
2 answers:
Vlad1618 [11]2 years ago
8 0
The solution is :
x= -8/3 , -2
Murrr4er [49]2 years ago
3 0

Answer:

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

Step-by-step 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:

<em>a</em> = 3, <em>b</em> = 14, and <em>c</em> = 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.

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