math
posted by alicia .
identify all real roots of x^39x^2+16x8=0

let f(x) = x^39x^2+16x8
try x = ±1, ±2, ±4, ±8 , hoping to get f(x) = 0
wow, after one try ...
f(1) = 1  9 + 16  8 = 0
so x1 is a factor
using synthetic division I had the other factor as
x^2  8x + 8
so x^2  8x + 8 = 0
I will use completing the square , since the middle term is even
x^2  8x + 16 = 8 + 16
(x4)^2 = 8
x4 = ±√8 = ± 2√2
x = 4 ± 2√2 or x = 1
Respond to this Question
Similar Questions

Math
Which describes the number and type of roots of the equation x^2625=0? 
Algebra II
Which describes the number and type of roots of the equation x^2 625=0? 
Precalculus
"Show that x^6  7x^3  8 = 0 has a quadratic form. Then find the two real roots and the four imaginary roots of this equation." I used synthetic division to get the real roots 2 and 1, but I can't figure out how to get the imaginary … 
Precal
let P(x)=2x^4x^3+13^28x24. Use synethetic division to show that x+1 is a factor of P(x) Answer:2x^33x^2+16x24 Then find all real and imaginary roots of P(x)=0. 
mathematics
Use the discriminant to determine the number of real roots the equation has. 3x2 – 5x + 1 =0 A. One real root (a double root) B. Two distinct real roots C. Three real roots D. None (two imaginary roots) 
maths2
Use the discriminant to determine the number of real roots the equation has. 7x2 + 3x + 1 =0 A. One real root (a double root) B. Two distinct real roots C. Three real roots D. None (two imaginary roots) 
PreCalc/Trig...
Helpp needed, this is sort of confusing me. Describe the nature of the roots for this equation. 2x^2x+1=0 A. Two real, rational roots B. Two real, irrational roots C. One real, double root D. Two complex roots 
Algebra 2/Trigonometry
How do I solve f(x)=x^36x^2+16x96 using Descartes' Rule of Signs to find the number of positive and negative real roots, along with imaginary roots, but not with a graph? 
algebra
if a quadratic equation with real coefficents has a discriminant of 10, then what type of roots does it have? 
Math
Given that the equation x(x2p)=q(xp) has real roots for all real values of p and q. If q=3, find a nonzero value for p so that the roots are rational.