If α and β are the roots of $x^2-5x+6=0$, the quadratic equation whose roots are 2α and 2β is:

α + β = 5 and αβ = 6, so the new roots have sum 2α + 2β = 10 and product (2α)(2β) = 4αβ = 24. The equation is $x^2-10x+24=0$. (The roots 2 and 3 double to 4 and 6, and 4 + 6 = 10, $4\times 6=24.$)