If ` alpha, beta ` are the roots of ` x^(2) - 3x + a = 0 , a in R and lt 1 lt beta,`
then find the values of a

Explanation

To solve the problem, we need to find the values of \( a \) such that the roots \( \alpha \) and \( \beta \) of the quadratic equation \( x^2 - 3x + a = 0 \) satisfy the condition \( 1 < \alpha < \beta \).

### Step 1: Identify the roots of the quadratic equation
The roots of the quadratic equation \( x^2 - 3x + a = 0 \) can be found using the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Here, \( a = 1 \), \( b = -3 \), and \( c = a \). Thus, the roots are:
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