Show that the equation $$2x^3-3x^2-2x+5=0 $$ has a root between -1.5 and -1

SOLVING EQUATIONS NUMERICALLY

Question

Show that the equation $$2x^3-3x^2-2x+5=0 $$ has a root between -1.5 and -1

SOLVING EQUATIONS NUMERICALLY

anonymous · Answer

plug in x = -1.5 and x = -1 into the expression.  if one answer gives a positive and the other a negative, this proves that the function 2x^3-3x^2-2x+5 passes through the x-axis somewhere between x=-1.5 and x=-1

anonymous · Answer

And, what if you didn't have the -1.5 and -1?

anonymous · Answer

Then you'd have to factor, and that seems ugly.

anonymous · Answer

Well, no, then you know it doesn't have a root there. But if you wanted the actual solution, you'd have to factor.

anonymous · Answer

hmm. i guess you could look for the min of the function but we're doing this numerically?

anonymous · Answer

Yes, numerically. Ok. Thanks for the help. If a harder question comes up, I'll ask again :)

anonymous · Answer

of course, this could occur (and positive results, also):
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