I am stumbling on an (at first sight) simple homework example. Maybe someone can help me. I just would need tips how to build up the equations for the respective polynomials, not the full solution.
Here is the homework example: An even polynomial of fourth degree $f(x)$ has a zero point at $(-2,0)$ and on another zero point it has a tangent with the equation $y = 6 - 6 \cdot x$. The polynomial of second degree $g(x)$ is intersecting with $f(x)$ at a maximum of $f(x)$, furthermore $g(x)$ itself has a maximum at $(0.5,5.25)$.
The task is now to determine the polynomials $f(x)$ and $g(x)$, so to determine their coefficients. So I have to determine the three coefficients of $f(x) = a_1 \cdot x^4 + a_2 \cdot x^2 + a_3$ and the three coefficients of $g(x) = b_1 \cdot x^2 + b_2 \cdot x + b_3$.
So how to get the needed three equations for determining $a_1,a_2,a_3$ and the three equations for determing $b_1,b_2,b_3$ ?