# finding rational zeros of a function

• Mar 27th 2012, 05:14 PM
noork85
finding rational zeros of a function
ok the problem states find all rational zeros of the function f(x)= 2x^4-15x^3+23x^2+15x-25
i got:

P:-1,+1
q: -1,+1,-5,+5,+25,-25,

there are additional factors for the constant, what are they and how do i go about finding them? i dont want pts taken off from my exam by not finding ALL the factors.

and when i solve this problem, should i use the quadratic function or should i continue using synthetic division until its completely factorized? i got the answer, i just continued using synthetic division, i see that u can also use the quadratic function, question is does it matter what i use?

thanks!
• Mar 27th 2012, 05:36 PM
skeeter
Re: finding rational zeros of a function
Quote:

Originally Posted by noork85
ok the problem states find all rational zeros of the function f(x)= 2x^4-15x^3+23x^2+15x-25
i got:

P:-1,+1
q: -1,+1,-5,+5,+25,-25,

there are additional factors for the constant, what are they and how do i go about finding them? i dont want pts taken off from my exam by not finding ALL the factors.

and when i solve this problem, should i use the quadratic function or should i continue using synthetic division until its completely factorized? i got the answer, i just continued using synthetic division, i see that u can also use the quadratic function, question is does it matter what i use?

thanks!

if p indicates factors of the leading coefficient, then you forgot the factors of 2 ...

once synthetic division gets you down to a quadratic, then use the method you find easiest for determining the remaining zero(s).
• Mar 27th 2012, 05:38 PM
noork85
Re: finding rational zeros of a function
i thought u only factor the constant, that being 25.
• Mar 27th 2012, 05:49 PM
noork85
Re: finding rational zeros of a function
ok so

factors of constant are:+-1,+-5,+-25
factors of coefficient are:+-1,+-2
possible zeros are obtained by dividing the factors of constant by factors of coefficient? and they are,
+-,+-5,+-25,+-,1/2,+-5/2,+-25/2

is there an easier way to obtain the possible zeros when u have alot to divide?
• Mar 27th 2012, 05:55 PM
skeeter
Re: finding rational zeros of a function
Quote:

Originally Posted by noork85
ok so

factors of constant are:+-1,+-5,+-25
factors of coefficient are:+-1,+-2
possible zeros are obtained by dividing the factors of constant by factors of coefficient? and they are,
+-,+-5,+-25,+-,1/2,+-5/2,+-25/2

is there an easier way to obtain the possible zeros when u have alot to divide?

I always start with the easy candidates ... $\displaystyle \pm 1$ ... I note that x = 1 is a zero right off

you can also use the intermediate value theorem to find intervals that have zeros.
• Mar 27th 2012, 05:58 PM
noork85
Re: finding rational zeros of a function
can u please demonstrate that with this example?
• Mar 27th 2012, 06:06 PM
skeeter
Re: finding rational zeros of a function
Quote:

Originally Posted by noork85
can u please demonstrate that with this example?

$\displaystyle f(x)= 2x^4-15x^3+23x^2+15x-25$

$\displaystyle f(2) = 9$ , $\displaystyle f(3) = -16$

since f(x) is a continuous polynomial function, this tells you you have a zero between x = 2 and x = 3 ... try x = 5/2