SOLUTION: -3x^4-7x+17=0 how many complex roots does this polynomial equation have?

Question 1147243: -3x^4-7x+17=0 how many complex roots does this polynomial equation have?
Found 2 solutions by Boreal, rothauserc:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
this has one sign change with original function, so it has one positive root.
with -x for x
-3x^4+7x+17=0
this also has one sign change, so there is one negative root. That leaves two other roots in this fourth power function and they are conjugate complex roots.
Two.

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
-3x^4 -7x +17 = 0
:
The Fundamental Theorem of Algebra says that this equation will have 4 roots(this is the degree of the polynomial)
:
The Rational Roots Theorem says that if this equation has rational roots, then
:
q could be +or - 1, + or - 3
:
p could be + or - 1, + or - 17
:
x = + or - 1, + or - 17, + or - 1/3, + or - 17/3
:
none of these possible roots satisfy the equation, therefore
:
we consider the graph of the equation
:

:
Therefore, this equation has 2 complex roots and 2 rational roots
:
if we wanted to determine all the roots for x, then we would turn to using Newton's method for finding the rational roots first
:
RELATED QUESTIONS
How many complex roots does the polynomial equation have? 5x^3−4x+1=0... (answered by MathLover1,ikleyn)
How many complex roots does the polynomial equation have? 5x^3 - 4x + 1 = 0 A. 2 (answered by math_helper,Alan3354)
How many complex roots does the equation below have? x 6 + x 3 + 1 =... (answered by Edwin McCravy,ikleyn)
How many roots does 2xsquared-7x-5=0... (answered by solver91311)
How many complex roots does 5x6 + x4 3 = 0 have? (Points : 4) 3 4 (answered by MathLover1)
How many complex, real, and rational roots does the following polynomial have:... (answered by MathLover1)
how many roots does a fifth degree polynomial equation have?... (answered by stanbon)
How many roots does this equation have?... (answered by jim_thompson5910)
according to descartes rule of signs,(a) how many positive roots does this equation have... (answered by Nate)