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

Question

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

Answer 1

it's a 2nd order polynomial ... there are only two roots

your list of "actual roots" is the answer to the question
... how many are there?

Answer 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 ?

Answer 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

Answer 4

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

Answer 5

That does not make sense to me at all

Answer 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

Answer 7

the question is asking about POSSIBLE rational roots

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

Answer 8

LOL, thanks R Scott !