α and β are the zeroes of $x^2+3x-4$. A new quadratic polynomial (leading coefficient 1) has 3α and 3β as its zeroes. What is it?

$\alpha +\beta =-3$ and $\alpha \beta =-4$. New sum $=3\alpha +3\beta =3(-3)=-9$; new product $=(3\alpha )(3\beta )=9\alpha \beta =-36$. Polynomial $=x^2-(-9)x+(-36)=x^2+9x-36$. (The zeroes 1 and −4 become 3 and −12.) $x^2-9x-36$ flips the sign of the new sum; $x^2+9x-12$ multiplies the product by 3 instead of by $3^2$; $x^2+3x-36$ leaves the sum unscaled.