Rational Zero theorm
~ How many possible rational zeros.
~p- constant term- number w/o x
~q- leading coefficient
~p- constant term- number w/o x
~q- leading coefficient
Application
The water level in a bucket sitting on a patio can be modeled by f(x)=x^3+4x^2-2x+7, where f(x) is the height of the water in millimeters and x is the time in days. On what day(s) will the water reach 10 millimeters. Put 10 in for f(x)
P~3=+-1,+-3
Q~1=+-1
P/Q=+-1,+-3
*plug in y, find where 0 is
or
You can use synthetic division
The water level in a bucket sitting on a patio can be modeled by f(x)=x^3+4x^2-2x+7, where f(x) is the height of the water in millimeters and x is the time in days. On what day(s) will the water reach 10 millimeters. Put 10 in for f(x)
P~3=+-1,+-3
Q~1=+-1
P/Q=+-1,+-3
*plug in y, find where 0 is
or
You can use synthetic division
Descartes' Rule of Signs
-How Many, positives, negatives
- The number of positives = to # of positive sign changes in origional function
- The # of negative = when you plug in f(-x)
* neg- if exponent is odd change coefficient to opposite sign.
- The number of positives = to # of positive sign changes in origional function
- The # of negative = when you plug in f(-x)
* neg- if exponent is odd change coefficient to opposite sign.