Let $M_{n \times n}$ be the set of all $n\times n$ symmetric matrices such that the characteristic polynomial of each $A\in M_{n\times n}$ is of the form
$t^n+t^{n−2}+a_{n−3}t^{n−3}+⋯+a_1t+a_0.$
Then the dimension of $M_{n\times n}$ over $\mathbb{R}$ is
a) $(n−1)n/2$
b) $(n−2)n/2$
c) $(n−1)(n+2)/2$
d) $(n−1)^2/2$
For general symmetric matrices the dimension will be $n(n+1)/2$. What will it be here?