math

What is the number of distinct possible rational roots of the polynomial P(x)=5x2+19x−4

i know that the actual roots of the polynomial are ±1,±1/5,±2,±2/5,±4,±4/5 through finding the rational roots but I am confused on what the question is asking by saying the possible distance.

The choices are 6,12,5, or 10

1. 👍
2. 👎
3. 👁
1. it's a 2nd order polynomial ... there are only two roots

... how many are there?

1. 👍
2. 👎
2. HUH ?
if
y = 5 x^2 + 19 x - 4
the roots are when y = 0
5 x^2 + 19 x - 4 = 0
(5x-1)(x+4) = 0
x = 1/5 and x = -4

the polynomial that has all the roots you gave is
(x-1)(+1)(5x-1)(5x+1)(x-2)(x+2) (5x-2)(5x+2) .....
Typo or something ?

1. 👍
2. 👎
👤
Damon
3. ±1,±1/5,±2,±2/5,±4,±4/5 are all the roots I came to the conclusion of but the choices they are giving me are 6,12,5, or 10 to find f distinct possible rational roots of the polynomial

1. 👍
2. 👎
4. There are only two roots of a polynomial that has x^2 as the highest power of x in it.

1. 👍
2. 👎
👤
Damon
5. That does not make sense to me at all

1. 👍
2. 👎
6. Well you have a typo or something.
A polynomial like
a x^2 + b x + c
can only cross the x axis twice, maximum. (If it never crosses, roots have imaginary parts)
like if polynomial is x^2 + 10
that is zero when x = +/- sqrt( -10) which is +/- i sqrt (10)
if x^2 + x + 10
then
[-1 +/-sqrt(-39) ] / 2

1. 👍
2. 👎
👤
Damon

for the general equation ... f(x) = a x^2 + b x + c
... the POSSIBLE rational roots are ... (factors of c) / (factors of a)

1. 👍
2. 👎
8. LOL, thanks R Scott !

1. 👍
2. 👎
👤
Damon

Similar Questions

1. algebra

a polynomial equation with rational coefficients has the roots 7+sgrt3, 2-sgrt6 find two additional roots 7-sgrt3, 2+sgrt6 3-sgrt7, 6+sgrt2 7+sgrt3, 2-sgrt6 3+sgrt7, 6=sgrt2 could someone help

2. Alegbra 2

Use the rational root theorem to list all possible rational roots for the equation. X^3+2x-9=0. Use the rational root theorem to list all possible rational roots for the equation. 3X^3+9x-6=0. A polynomial function P(x) with

3. algebra

How can you quickly determine the number of roots a polynomial will have by looking at the equation?

4. Math

A jewelry box is designed such that its length is twice its width and its depth is 2 inches less than its width. The volume of the box is 64 cubic inches. Use synthetic division to find the roots of the polynomial equation. Are

Use the value of the discriminant to determine the number and type of roots for the equation: (x^2+20=12x-16) 1 real, irrational 2 real, rational no real 1 real, rational

2. Algebra 2

Find a third-degree polynomial equation with rational coefficients that has roots -1 and i+1

3. Algebra

Solve the given polynomial equation. Use the Rational Zero Theorem and​ Descartes's Rule of Signs as an aid in obtaining the first root. 2 x cubed minus 5 x squared minus 5 x minus 1 equals 02x3−5x2−5x−1=0

4. algebra

if a quadratic equation with real coefficents has a discriminant of 10, then what type of roots does it have? A-2 real, rational roots B-2 real, irrational roots C-1 real, irrational roots D-2 imaginary roots

if the roots of ax^2+bx+c=0 are real, rational, and equal, what is true about the graph of y= ax^2+bx+c? 1.) it intersects the x-axis at two distinct points. 2.) it lies entirely below the x-axis 3.) it lies entirely above the

2. math ~dont know all but check some~ pls help!!!

1. Draw a model to represent the polynomial x2 + 2x + 4. (1 point) 1 big square, 1 tall rectangle, 4 little sqaures 1 big square, 2 tall rectangles, 4 little sqaures in the shape of an "L" 2 big sqaures, 4 little squares none of

3. Algebra 2

1) Find the roots of the polynomial equation. x^3-2x^2+10x+136=0 2) Use the rational root theorem to list all problem rational roots of the polynomial equation. x^3+x^2-7x-4=0. Do not find the actual roots.

4. Algebra

Find a polynomial equation with real coefficients that has the given roots. 5 and -7i Write a polynomial equation with roots 5 and -7i x^3 - __ x^2 + __ x -__ = 0