Descartes’ Rule of Signs - Guided Notes
Descartes’ Rule of Signs
If P  x  is a polynomial with real coefficients, then
1.
the number of positive real zeros of P  x  is either equal to the number of
variations in sign of P  x  or is less than that number by a positive even integer ;
2.
the number of negative real zeros of P  x  is either equal to the number of
variations in sign of P   x  or is less than that number by a positive even integer .
Descartes’ Rule of Signs gives you information about the number of positive and negative real zeros of
a polynomial function.
Note 1
A variation in sign occurs whenever adjacent coefficients have opposite signs.
Ex
Determine the possible number of positive zeros, negative zeros, and imaginary zeros of
P  x   x 4  3x3  2 x 2  x  5 . Summarize the possibilities in a table.
Solution
P  x   x4  3x3  2 x2  x  5 has _____ variation(s) in sign.
Therefore, P  x  has _____________________________________________________
P   x     x   3  x   2   x     x   5
4
3
2
P   x   x4  3x3  2 x 2  x  5 has _____ variation(s) in sign.
Therefore, P  x  has _____________________________________________________
Possibilities:
positive zeros
negative zeros
imaginary zeros
BW – R0812