# Tanishq's roots

Algebra Level 4

Real numbers $$w\leq x\leq y\leq z$$ satisfy

\begin{align} w+x+y+z&=12\\ wx+wy+wz+xy+xz+yz&=17\\ wxy+wxz+wyz+xyz&=-114\\ wxyz&=-216. \end{align}

Consider the polynomial $g(u)= wu^3+xu^2+yu+z.$

The equation $$g(u) = 0$$ has roots $$p, q, r$$. The value of $$p^2 + q^2 + r^2$$ can be written as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers. What is the value of $$a+b$$?

This problem is posed by Tanishq A.

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