This is the question I have in front of me. Clearly, I need to find the range of values of $x$ for the given inequality.
Having taken a cue from a similar question, here's how I approached it -
Let $ a = x^2 + 3x + 1$ $\implies ax^2 + 3ax - (3a + 5) \geq 0$
Now, for this quadratic expression to be greater than or equal to $0$, the coefficient of $x^2$ must be $>0$, with the discriminant being equal to $0$. But, the coefficient of $x^2$ i.e. $a = x^2 + 3x + 1$ can take negative values also, which does not ensure the requirement.
So, how shall I go about this one? Any help will be appreciated. Thanks.