If `alpha` and `beta` are the zeros of the quadratic polynomial `f(x)=2x^2-5x+7` , find a polynomial whose zeros are `2alpha+3beta` and `3alpha+2beta` .

Explanation

To find a polynomial whose zeros are \(2\alpha + 3\beta\) and \(3\alpha + 2\beta\) given that \(\alpha\) and \(\beta\) are the zeros of the quadratic polynomial \(f(x) = 2x^2 - 5x + 7\), we can follow these steps:

### Step 1: Identify the coefficients and calculate the sum and product of the roots
The given polynomial is \(f(x) = 2x^2 - 5x + 7\).

Using the relationships between the coefficients and the roots:
- The sum of the roots \(\alpha + \beta\) is given by:
\[
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