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 the quadratic polynomial \(f(x) = 2x^2 - 5x + 7\) with zeros \(\alpha\) and \(\beta\), we can follow these steps:

### Step 1: Find the sum and product of the zeros \(\alpha\) and \(\beta\)

The sum of the roots \(\alpha + \beta\) can be calculated using the formula:
\[ \alpha + \beta = -\frac{\text{coefficient of } x}{\text{coefficient of } x^2} = -\frac{-5}{2} = \frac{5}{2} \]
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