What hope does Banquo maintain in Act 3, scene 1?

Here's the passage you ask about from Act 3.1 in
Shakespeare's Macbeth:

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Thou hast it now--King, Cawdor, Glamis,
all

As the Weird Women promised, and I
fear

Thou played'st most foully for't.  Yet it was
said

It should not stand in thy
posterity,

But that myself should be the root and
father

Of many kings.  If there come truth from
them--

As upon thee, Macbeth, their speeches
shine--

Why, by the verities on thee made
good,

May they not be my oracles as
well,

And set me up in hope?  But hush, no more.  (Act
3.1.1-10)

Banquo's hope is,
unfortunately, tied up with his suspicions.  He knows about the witches' predictions,
which makes him suspicious of Macbeth.  This makes him a danger to the new
king. 

But the same witches that predict Macbeth will be
king, also predict Banquo's heirs will be king.  This is Banquo's
hope. 

Banquo is a bit ambitious, as Macbeth is.  He would
like to keep his name at the forefront of Scotland's leadership, and he would like to
have his sons be kings.  This is important in the context of the play because Banquo
serves as a foil to Macbeth.  Faced with a similar situation, though Banquo would like
to see the predictions fulfilled, he is not willing to go to the lengths that Macbeth is
to make them come true.