SOLUTION: Find all the rational zeros of the function f(x)=5x^4-15x^3-265^2-45x

Question 1067432: Find all the rational zeros of the function f(x)=5x^4-15x^3-265^2-45x
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
5x^4-15x^3-265x^2-45x
factor out a 5x
5x(x^3-3x^2-53x-9)=0 notice I wrote 265x^2
x=0 is one root.
synthetic division
1===-3===-53===-9 try 9
1====6===1======0
(x-9)(x^2+6x+1)=0
x=9 is a second root
x=(1/2)(-6 +/- sqrt (36-4)); sqrt (32)=4 sqrt(2))
x=-3+/- 2 sqrt (2), the other two roots, numerically about -5.8 and -0.2

RELATED QUESTIONS
identify all rational zeros of the polynomial function... (answered by Fombitz)

Using the rational zeros theorem, list all possible rational zeros for the given... (answered by ReadingBoosters)

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use (answered by lwsshak3)

find all of the rational zeros of this function f(x) = x^4 -... (answered by nabla)

List all of the potential rational zeros of the polynomial function. Do not attempt to... (answered by fractalier)

Find all the rational zeros of the function f(x)=36x^4+66... (answered by Fombitz,ewatrrr)

find a rational zero of the polynomial function and use it to find all the zeros of the... (answered by stanbon)

List all possible rational zeros of f using the rational zero theorem. Then find all the... (answered by nyc_function)

Find all the rational zeros of the function f(x)=8x^4-24x^3-424x^2-72x (answered by Edwin McCravy)