Let f(x) a quadratic polynomial with leading coeffient 1 such that f(0)=p and p ≠ 0. f(1)= 1/3. If equation f(x)=0 and f ∘ f ∘ f ∘ f(x)=0 have a common root then find f(-3)

Algebra question

Medium · from the problemset algebra collection

$$\text{Let } f(x) \text{ a quadratic polynomial with leading coeffient 1 such that } f(0)=p \text{ and } p\neq0. \\ f(1)=\frac{1}{3}. \text{ If equation } f(x)=0 \text{ and } f\circ f\circ f\circ f(x)=0 \text{ have a common root then find } f(-3)$$

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