help - if p/q is a rational zero... (1 Viewer)

[bos1234]

if p/q is a rational zero of p(x), then p is a factor of the sontant polynomial ao and q is a factor of the leading coeffecient an

But there are so many different combination of factors. Is it trial and error or is there any short cut?

 

[pLuvia]

What's the question?

 

[bos1234]

d/w i know how to do it.. but how do i do this qn.. keep getting 0

 

[SoulSearcher]

Simpler, you know that two of the roots are i and -i. You know the constant term is 3. Thus, by product of roots, letting g and h being the other two roots,

-i²gh = 3
gh = 3

Since one of the roots is rational, roots can be either -3 and -1 or 1 and 3, but since the sum of the roots is negative, roots have to be -3 and -1. Therefore the roots of the equation are i, -i, -3, -1, and the factorisation is (x²+1)(x+3)(x+1) I think that's how it's done, may be horribly wrong though.

 

[bos1234]

ahh kk

yeah ur answer is the same

thanks bye​