SOLUTION: P(X)=x^3-3x^2-5x+10 A) Evaluate P(x) for integers -3 through 5 B) Find all of the zeros of P(x) C) Prove that five is an upper bound on the zeros of P(X)

Question 918970: P(X)=x^3-3x^2-5x+10
A) Evaluate P(x) for integers -3 through 5
B) Find all of the zeros of P(x)
C) Prove that five is an upper bound on the zeros of P(X)
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

A) Evaluate for integers through :

=

B) Find all of the zeros of

one zero is:
=>
...use quadratic formula to find other two zeros:

solutions:

and

so, zeros are:,, and

C) Prove that five is an upper bound on the zeros of

to find bounds for the real roots of the polynomial means we are looking for a number that is greater than all roots (an upper bound) and a number that is less than all roots (a lower bound)
we are looking if is greater than all roots
zeros are:
,
, and

so, it's proven that is an upper bound on the zeros of

graph of :

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