# rational zeros theorem

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers.
f(x)=25x^4+26x^3+126x^2+130x+5
Find the real zeros
x=
Use the real zeros to factor f
f(x)=

1. 👍 0
2. 👎 0
3. 👁 327
1. only possible rational roots are
x = ±1, ±1/5, ± 1/25

quickly found x=-1 to work
so one factor is x+1

after reducing it to a cubic by synthetic division, it took a bit longer to find x = -1/25 to work
so (25x+1) is another factor
long algebraic divsion gave the last factor as x^2 + 5, which has no real roots.

so real roots are
x = -1 and x = -1/25

1. 👍 0
2. 👎 0
2. just a note:
Things worked out in this case, but x = ±5 were also candidates, since 5/1 has suitable numerator and denominator. For example,

25x^4-100x^3-124x^2-4x-5
has similar coefficients, but has real roots -1 and 5:
(x+1)(x-5)(25x^2+1)

1. 👍 0
2. 👎 0
3. given that f(x) = 9/x-5 and g(x) = 12/x+12 find

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Precalculus

Suppose that a polynomial function of degree 4 with rational coefficients has i and (-3 + square root of 3)as zeros find the other zeros

2. ### Algebra 2!!!!

Use the graph to shorten the list of possible rational zeros of the function. Then find all real zeros of the function. 1.) f(x)= 4x^3-8x^2-15x+9 4.) f(x)= 2x^3-5x^2-4x+10

3. ### Math

Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function. -2x^4+4x^3+3x^2+18

4. ### Algebra

Could you please check my answers? Find an nth degree polynomial function with real coefficients satisfying the given conditions. 1. n=3; 3 and i are zeros; f(2)=20 -I got: f(x)=-4^3+12x^2-4x+12 3.n=3;4 and i zeros;f(-3)=60 -I

1. ### algebra

Using the rational zeros theorem to find all zeros of a polynomial The function below has at least one rational zero. Use this fact to find all zeros of the function h(x)=7x^4-9x^3-41x^2+13x+6 if more than one zero, separate with

2. ### Algebra

Use the Rational Zero Theorem to list all the possible rational zeros of f(x) = 2x^4 + 3x^3 - 9x^2 + 3x + 10 DO NOT attempt to find the zeros.

3. ### pre-ap Algebra 2

write a polynomial function f of least degree that has the rational coefficients, a leading coefficient of 1, and the given zeros. Given zeros: -2,2,-1,3, sqrt 11

4. ### Math

Use the given information about a polynomial whose coefficients are real numbers to find the remaining zeros of the polynomial. Degree: 6 Zeros: -6 + 13i^3, -8 + s^2i, -3 - 4i

1. ### Precalculus

There is at least one polynomial with real functions with 9+i as its only nonreal zero. A. The statement is​ false, because the Fundamental Theorem of Algebra dictates that there must be n complex zeros for a polynomial of

2. ### college algebra--need help please!!

information is given about a polynomial f(x)whose coefficients are real numbers. Find the remaining zeros of f. degree:5, zeros: -6, 6-i please help and show all work.

3. ### algebra 2

help please!! state the possible rational zeros for each function. then find all zeros. y=x^3-13x^2-x+13 show all the step please .thanks

4. ### calculususe the rational zeros theorem to list the

use the rational zeros theorem to list the potential rational zeros of the potential function. Do not attempt to find the zeros. f(x)=2x^5-x^3+8x^2+52