Question

When asked to find the zeros of the function r(t) = 5t3 – 8t2 + 7t + 2 which task would you complete first - Rational Root Theorem or Descartes’ Rule of Signs? Use complete sentences to explain your reasoning.


I just need help finding P since I'm having a hard time testing the negatives.

Answer 1

You could use Descartes' first, but I usually bypass that and go straight to RRT.

Answer 2

That's what I did but for some reason I'm having difficulty doing the negative numbers of P

It is =- 1, +-2, 2/5 and +- 1/5 right?

Answer 3

What do you mean by "negative numbers of P" What is P representing here?

Answer 4

From RRT, the possible rational roots are {-2, -1, -2/5, -1/5, 1/5, 2/5, 1, 2}

Answer 5

P = +-5

Q = +- 1, +-2, +- 2/5, +- 1/5 Is this correct?

Answer 6

But how do do -2/5 then? I know hot to the whole numbers :P

Answer 7

The usual notation I see is that the rational numbers are in the form p/q where p=constant and q=leading coefficient. Is that what you mean?
Are you now asking how to test -2/5 as a possible root?

Answer 8

Yes, how do I test it.

Answer 9

Same was as with the integers, use synthetic evaluation.

Answer 10

Bad news for this one. There are no rational roots. DRS says 1 negative real root and 0 or 2 positive real roots. From the graph, it looks like there are no positive real roots.
There is only one in the vicinity of -0.23