Given:
The equation is:
The graph of the and
are given on a coordinate plane.
To find:
The solution of the given equation from the given graph.
Solution:
From the given graph it is clear that the graphs of and
intersect each other at points (1.24,5.24) and (16,20).
It means the values of both functions and
are equal at
and
.
So, the solutions of given equation are and
.
Therefore, the correct option is only F.
There seems to be one character missing. But I gather that <em>f(x)</em> needs to satisfy
• divides
• divides
I'll also assume <em>f(x)</em> is monic, meaning the coefficient of the leading term is 1, or
Since divides
, and
where is degree-2, and we can write it as
Now, we have
so if divides
, then
is degree-2, so
is degree-4, and we can write
where is degree-1.
Expanding the left side gives
and dividing by leaves no remainder. If we actually compute the quotient, we wind up with
If the remainder is supposed to be zero, then
Adding these equations together and grouping terms, we get
Then , and you can solve for <em>a</em> and <em>b</em> by substituting this into any of the three equations above. For instance,
So, we end up with