Suppose a polynomial function which represents water level in the lake is given by:
W(x)=(x-1) (Ax-B)(C x -D)(P x -Q)( x -S), which is polynomial function of degree 5, showing water level on five different days.
As, temperature will vary on different days, so water level will change in the lake at different days of month or year.
X intercepts can be found by,
Put , W(x) =0
(x-1) (Ax-B)(C x -D)(P x -Q)( x -S)=0
→x-1=0,∧ Ax-B=0,∧C x -D=0,∧P x-Q=0, ∧ x-S=0
→x=1, [tex]x=\frac{B}{A}, x=\frac{D}{C}, x=\frac{Q}{P}, x=S\\\\ 1<\frac{B}{A}<\frac{D}{C}<\frac{Q}{P}<S[/tex]
These are x intercepts.That is water level on five different days.
There are chances that water level in lake increase if rain happens, considering that there is no cats and dogs in between the period so, these are representation of water in lake on on five different days.
On, first day, that is ,when, x=1, there will be no change in water level in the lake.
As, graph of polynomial function is like this, but x intercepts will be just lines , x=1, x=B/A,... passing through these five points.
