SOLUTION: show that the polynomial has a zero between -4 and -3
x to the 4th power minus 4x to the third power minus 20x squared plus 32x minus 12
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Question 1032931: show that the polynomial has a zero between -4 and -3
x to the 4th power minus 4x to the third power minus 20x squared plus 32x minus 12
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ =\ x^4\ -\ 4x^3\ -\ 20x^2\ +\ 32x\ -\ 12)
Bolzano's Theorem:
If 
is a continuous function in the closed interval 
with )
and )
of opposite sign, then \ :\ f(c)\ =\ 0)
Polynomial functions are continuous over the entirety of the Real numbers, therefore the given polynomial must be continuous over 
:
So calculate )
and )
. If \right)\ \not =\ \text{sgn}\left(P(-3)\right))
, then there is a value 
in the interval )
such that \ =\ 0)
.
John
My calculator said it, I believe it, that settles it
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