If \(\alpha\) and \(\beta\) are the two roots of the quadratic equation \(6x^2-5x+1=0\), then the sum of their squares will be:
\(\frac{13}{36}\)
By Vieta's formulas, for the equation \(6x^2-5x+1=0\), the sum of roots \(\alpha + \beta = 5/6\) and the product of roots \(\alpha\beta = 1/6\).
The sum of squares of the roots is \(\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta = (5/6)^2 - 2\times 1/6\).
This equals \(25/36 - 12/36 = 13/36\).
Hence, \(\frac{13}{36}\).
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