So here is the problem, $a$ and $b$ are two distinct real roots of $f(x)=0$ where $f(x)=x^4-6x+3$, show that $(a+b)^2$ is a root of $g(x)=x^3-12x-36$.
I have tried many methods, such as substitution, expanding the polynomial, changing it to different form, and reduce the power of $x$, but still could not make any process.
Can anyone help me for some suggestion?
Thank you very much.