It is known that the difference of the cubes of the roots of the quadratic equation $a x^{2}+b x+c=0$ is 2011. How many roots does the equation $a x^{2}+2 b x+4 c=0$ have?
From the condition, it follows that the first equation has two roots. Therefore, its discriminant $D=b^{2}-4 a c>0$. The simplified discriminant of the second equation is also equal to $b^{2}-4 a c$, so it also has two roots.

## Answer

Two roots.