precaculus help please

Question

Find all the rational zeros of the function f(x)=x5−7x4+19x3−37x2+60x−36

.

Select one:

a. x=2,-3,-1

b. x=-3,2

c. x=1,3

d. x=2,-2,3,1

Answer 1

Morgan, Lev overlooked the possibility of a root, such as 1 or 3, having multiplicity more than one. As David said, 1 and 3 work, and not 2. So (c) is the only possible answer.

So next time you see a problem like this, you might want to try all of the proposed roots in the list of answers.

Answer 2

The key here is that the polynomial should have exactly 5 roots, but complex roots comes in pairs

Choice d) is wrong - it leaves just one for complex roots

Choice b) c) are wrong - they leave 3 for the complex roots, so again no pairs

The only choice is a)

But you need to verify, of course, that the values listed are indeed roots

Answer 3

1) Use the Rational Root Theorem to list possible roots. In this case they are ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20±, ±30, ±60.

2) Use Synthetic substitution to determine roots and depressed polynomials.