Answer:
Option 3 - The given equation is a prime.
Step-by-step explanation:
Given : Quadratic equation 
To find : The factors of given equation.
Solution : To factories the given equation 
We will apply discriminant method
General form - 

Solution is 
Equation is 
where a=3 , b=1, c=7




Solution is 



Therefore, The factors are
![[x+(\frac{-1+\sqrt{83}i}{6})][x-(\frac{-1-\sqrt{83}i}{6})]](https://tex.z-dn.net/?f=%5Bx%2B%28%5Cfrac%7B-1%2B%5Csqrt%7B83%7Di%7D%7B6%7D%29%5D%5Bx-%28%5Cfrac%7B-1-%5Csqrt%7B83%7Di%7D%7B6%7D%29%5D)
So, 1,2,4 are not the options.
Now, check for prime
In a quadratic equation if
form a complete square then it is not prime and vice-versa.
In this question
does not make a perfect square.
Therefore, It is a prime.
Option 3 is correct.