If the roots of the equation \(x^2 - 2x + 1 = 0\) are \(\alpha\) and \(\beta\), then the equation whose roots are \(\alpha^2\) and \(\beta^2\) will be:
\(x^2 - 2x + 1 = 0\)
The given equation \(x^{2} - 2x + 1 = 0\) factorises as \((x - 1)^{2} = 0\), so its roots are \(\alpha = \beta = 1\).
The new roots are \(\alpha^{2}\) and \(\beta^{2}\), both equal to \(1^{2} = 1\).
An equation with both roots equal to 1 is again \((x - 1)^{2} = 0\), which expands to \(x^{2} - 2x + 1 = 0\).
Hence, the required equation is \(x^{2} - 2x + 1 = 0\).
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