Question 1147243
this has one sign change with original function, so it has one positive root.
with -x for x
-3x^4+7x+17=0
this also has one sign change, so there is one negative root.  That leaves two other roots in this fourth power function and they are conjugate complex roots.

Two.

{{{graph(300,300,-10,10,-100,30,-3x^4-7x+17)}}}