Prove that for any value of a, the inequatiion `(a^(2)+3)x^(2)+(a+2)x-6lt0` is true for atleast one negative `x`.

Explanation

To prove that the inequality \((a^2 + 3)x^2 + (a + 2)x - 6 < 0\) is true for at least one negative \(x\) for any value of \(a\), we will follow these steps:

### Step 1: Define the quadratic function
Let
\[ f(x) = (a^2 + 3)x^2 + (a + 2)x - 6. \]
We need to show that there exists at least one negative \(x\) such that \(f(x) < 0\).
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