Question 1089558: Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function.
F(x)= 2x^3 -5x^2 +x+4
*2 or 0 positive zeros, 2 or 0 negative zeros
*3 or 1 positive zeros, 3 or 1 negative zeros
*2 or 0 positive zeros, 1 or 0 negative zeros
*2 or 0 positive zeros, 1 negative zero
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website! The rule states that if the terms of a single-variable polynomial with real coefficients are ordered by descending variable exponent, then the number of positive roots of the polynomial is either equal to the number of sign differences between consecutive nonzero coefficients, or is less than it by an even number.
So, coefficients are  , , , .
As can be seen there are changes; + (in front of 2) changes to -(in front of 5), then -(in front of 5) to +(in front of 1), and + (in front of 1) does not change because next sign is also + (in front of 4)
This means that there are or  positive real roots.
To find number of negative real roots substitute  with  in the given polynomial:  becomes  .
Coefficients are  ,, ,.
As can be seen there is change;
all signs are -, only - (in front of 1) changes to +(in front of 4)
This means that there is negative real root.
Answer:
* or positive real roots; negative real root
|
|
|
