If $\alpha$ and $\beta$ are roots of the quadratic equation $x^2 - 7x + 10 = 0$, find the quadratic equation whose roots are $\alpha^2$ and $\beta^2$.

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Step 1: From $x^2 - 7x + 10 = 0$: $\alpha + \beta = 7$, $\alpha\beta = 10$.
Step 2: $\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta = 49 - 20 = 29$.
Step 3: $\alpha^2\beta^2 = (\alpha\beta)^2 = (10)^2 = 100$.
Step 4: Quadratic equation with roots $\alpha^2$, $\beta^2$: $x^2 - (\alpha^2 + \beta^2)x + \alpha^2\beta^2 = 0$, i.e., $x^2 - 29x + 100 = 0$.

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