If one of the roots of the equation ax^{2}-4ax+15=0 is \frac{3}{2} , then what is the sum of the squares of the roots?

Explanation

Let the roots be \alpha and \beta. The sum of the roots \alpha + \beta = \frac{-(-4a)}{a} = 4. Given \alpha = \frac{3}{2}, we find \beta = 4 - \frac{3}{2} = \frac{5}{2}. The sum of their squares is \alpha^2 + \beta^2 = (\frac{3}{2})^2 + (\frac{5}{2})^2 = \frac{9}{4} + \frac{25}{4} = \frac{34}{4} = \frac{17}{2}.

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