Asked by Auzy
                 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
            
        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
Answers
                    Answered by
            R_scott
            
    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?
    
your list of "actual roots" is the answer to the question
... how many are there?
                    Answered by
            Damon
            
    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 ?
    
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 ?
                    Answered by
            Auzy
            
     ±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
    
                    Answered by
            Damon
            
    There are only two roots of a polynomial that has x^2 as the highest power of x in it.
    
                    Answered by
            Auzy
            
    That does not make sense to me at all
    
                    Answered by
            Damon
            
    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
    
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
                    Answered by
            R_scott
            
    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)
    
for the general equation ... f(x) = a x^2 + b x + c
... the POSSIBLE rational roots are ... (factors of c) / (factors of a)
                    Answered by
            Damon
            
    LOL, thanks R Scott !
    
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