SOLUTION: what is the number of complex roots, real roots and imaginary roots for this equation, x^3-6x^2+x+34=0
Algebra.Com
Question 443930: what is the number of complex roots, real roots and imaginary roots for this equation, x^3-6x^2+x+34=0
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Use the rational roots theorem. If a polynomial equation with rational coefficients has a rational root, then that root will be of the form 
where 
is an even divisor of the constant term of the equation and 
is an even divisior of the lead coefficient. Possible rational roots are 
, 
, 
, and 
.
Use synthetic division to find the first real and rational root. This is an equation of odd degree with rational coefficients, hence there must be at least one real root and it must be rational. Review the process of synthetic division at Purple Math: Synthetic Division Be certain to review all four pages.
The quotient from your successful synthetic division will provide the coeffients of a quadratic equation. From these coefficients, you can calculate the discriminant to determine the character of the remaining two roots.
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
Which describes the number and type of roots of the equation x^2 + 121x = 0
a) 1 real... (answered by richwmiller)
State the number of complex roots, imaginary roots, and real roots:
-2x^6 – x^2 + x – 7 (answered by Fombitz)
Which describes the number and type of roots of the equation x^2 + 121x = 0
a) 1 real... (answered by richwmiller)
Which describes the number and type of roots of the equation x^2 - 625 = 0?
a. 1 real (answered by checkley77)
f(x)=x^5-6x^4+11x^3-2x^2-12x+8 has (x-2) as a factor
determine which one of the... (answered by MathLover1,Edwin McCravy)
what are the complex zeros of y=X^3 I think the real zero is "0" and the other 2... (answered by solver91311)
What are the roots, both real and imaginary, of the equation... (answered by richard1234)
Find the descriminate of y = x^2 - 6x + 9 and decribe the nature of the roots.
a. -6;2 (answered by Alan3354)
If the value of the discriminant for this equation is 0, what is the nature of the roots... (answered by TimothyLamb)
