SOLUTION: Can you please state the positive real zeros, negative real zeros, and imaginary zero for this functions : r(x)=x^4-x^3-5x^2+6x+1
Algebra.Com
Question 533623: Can you please state the positive real zeros, negative real zeros, and imaginary zero for this functions : r(x)=x^4-x^3-5x^2+6x+1
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Can you please state the positive real zeros, negative real zeros, and imaginary zero for this functions : r(x)=x^4-x^3-5x^2+6x+1
**
Using the Rational Roots Theorem to find the zeros:
....0....|....1........-1........-5.........6.........1
....1....|....1..........0........-5.........1.........2
....2....|....1......... 1........-3.........0.........1
....3....|....1........ 2........ 1.........6.........19 (3 is upper bound)
....0....|....1........-1........-5.........6.........1
..-1....|....1........-2........-3.........3........-2 (real root between 0 and -1)
..-2....|....1........-3........1.........4.........-7
..-3....|....1........-4........7......-15.........46 (-3 is lower bound) (real root between-2 and -3)
Procedure above shows there are two real roots between 0 and -1 and between -2 and -3,
but they are not rational. I don't know how to find these two irrational real roots algebraically. The graphics program on my computer show these roots to be -0.2929 and -2.2740. The other two roots are non-real or imaginary. See graph below as a visual check.
RELATED QUESTIONS
State the number of positive real zeros, negative real zeros, and imaginary zeros for... (answered by Nate)
state the number of positive real zeros, negative real zeros, and imaginary zeros for... (answered by richwmiller)
State the possible number of positive real zeros, negative real zeros & imaginary zero of (answered by kev82)
I need help on this problem.
State the possible number of positive real zeros,... (answered by vleith)
State the number of positive real zeros, negative real zeros, and imaginary zeros for... (answered by Fombitz,stanbon)
State the number of positive real zeros, negative real zeros, and imaginary zeros for... (answered by Fombitz)
Use Descartes rule of signs to determine how many positive and how many negative real... (answered by mukhopadhyay)
State the number of positive real zeros, negative real zeros, and imaginary zeros for... (answered by rmromero)
Use Descartes's Rule of Signs to determine the possible number of positive and negative... (answered by MathLover1)