Explain

A quadratic polynomial with a leading coefficient of 1 looks like this:

f(x) = (x - a)(x - b) To make this even easier to read, let’s replace those Greek letters with a and b.

We use the clues given in the problem to find the actual numbers for a and b:

From f(0)=p: We find that a×b=p.From f(1)=1/3:

We get the equation (1−a)(1−b)=1/3

The problem says f(x)=0 and f(f(f(f(x))))=0* *share a root.

If we call that root a, then f(a)=0.

Plugging this into the chain:

f(f(f(f(a))))=f(f(f(0)))=f(f(p))=0*.*

For f(f(p)) to be 0, the result of f(p) must be one of our roots (a or b).

By solving (p - a)(p - b) = a along with our other equations, we find:

• b = 3
• a = 7/6

f(x) = (x - 7/6)(x - 3)

o find $f(-3)$, we just plug in -3 for x:

f(-3) = (-3 - 7/6)(-3 - 3)

f(-3) = (-25/6)(-6)

f(-3) = 25