If `x^2+2a x+a<0AAx in [1,2],` the find the values of `a`.

Explanation

To solve the inequality \( x^2 + 2ax + a < 0 \) for \( x \) in the interval \([1, 2]\), we can follow these steps:

### Step 1: Understand the inequality
The expression \( x^2 + 2ax + a \) represents a quadratic function in \( x \). Since the coefficient of \( x^2 \) is positive (which is 1), the parabola opens upwards. For the quadratic to be negative in the interval \([1, 2]\), it must be below the x-axis at both endpoints \( x = 1 \) and \( x = 2 \).

### Step 2: Evaluate the quadratic at the endpoints
We need to ensure that:
1. \( f(1) < 0 \)
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