PRECALCULUS MATH

Question

P(x)=x4-13x3+55x2-91x.

a. Without doing any other work (graphing or algebraic), predict the number of solutions to this equation. Explain how you determined the number of solutions. (SOLVED)

b. Use your graphing calculator to support your prediction. Explain how your graph supports or changes your answer to part a.(SOLVED)

c. Given that x=0 is a solution, how can you find other real solutions? If there are other real solutions, find them. Be sure to show how you know these are solutions.

d. Find any non-real solutions.

e. Write P(x) in factored form

f. Suppose

S(x)=P(-x).

What can you say about the solutions to

S(x)=0?

I just need C,D,E, AND F

Answer 1

Decartes rules of signs tells you there are no negative real roots.

For c:

The only possible rational roots are 1, 7 & 13

1 is not a root, try 7 by dividing x-7 into the cubic....which shows that 7 is a root.

Then you have a quadratic left with the discriminant less than 0

Therefore, your roots are 0, 7 and a pair of complex conjugates which you can get from the quadratic formula.

There are only 3 factors x(x-7) and the quadratic

For S(x) there are no positive real roots and again -1, -7, and -13 are the only possible rational roots.