# Math Help - Factors

1. ## Factors

Some help would be greatly appreciated, I'm at such a loss

2. A cubic equation has three linear factors.
in this case,two are same
hence
$x^3 + 3x^2 - 9x + c= (x-p)(x-p)(x-q)$
$x^3 + 3x^2 - 9x + c= x^3-(2p+q)x^2+(2pq+p^2)x-p^2q$
comparing the coefficients,
$2p+q=-3...[1]$
$2pq+p^2=-9...[2]$
$p^2q=-c...[3]$
we solve first two equations for p and q
from 1st equation $q=-3-2p$
substituting in second $2p(-3-2p)=-9$
hence,after rearraging and simplifying $p^2+2p-3=0$
which gives $p=-3,1$
hence from first equation, $p=-3,q=3$ or $p=1,q=-5$
if we substitute in third equation,we get $c=-27,5$

Keep Smiling
Malay