idk why i cant get this
#Innequalities and discriminant
spare aspen
<@&791435371564892232>
like i get it graphically
but algebraically it should work
if we had q(q+8)<0 then we say q<0 so q+8<0 q<-8
how tf is it q>-8
fierce shuttle
cuz graph
spare aspen
ALGEBRACALLY
fierce shuttle
too bad
fierce shuttle
your gonna have fun later then
fierce shuttle
there is a way but whats the point
spare aspen
there is a way but whats the point
if you know can you just tell me
i like being thorough
and understanding
im not a natural mathematician
fierce shuttle
ok
spare aspen
cool
fierce shuttle
for ab to be greater than 0 we note that a and b must be greater than 0 or a and b are less than 0 so written as inequalities we have
ab>0 (a * b is just the factorised form)
this means the following need to be true
a>0 and b>0 or
a<0 and b<0
in your example a = q and b = q+8 so we have
q>0 and q+8>0 which will be true for q>0
also we have q<0 and q+8<0 which is true for q<-8
i wrote this out then realised that its <0 not >0
still applies
just let a = -q
-q> 0 and q+8>0 gives -8<q<0 straight away
spare aspen
-q> 0 and q+8>0 gives -8<q<0 straight away
yeah how does it give this?
spare aspen
solve both inequalities
yeah i do
q(q+8)<0
q<0 and q+8<0 so q<-8 or q<0 so then the overall answer should be q<0 since that includes q<-8 ,if i just looked at this purely algebraically.
fierce shuttle
no
for the product of two numbers to be less than 0 you need them to have opposite signs
i did it wrong
the first explanation was for >0
which still applies if u multiply the equation by -1
but for this
since u need them to have opposite signs
q > 0 and q + 8 < 0 is true or
q < 0 and q + 8 > 0 is true
wait im confusing myself now
ok thats not working for some reason
so ignore that
first bits right though
ab>0
to get the equation in that form u multiply by -1
giving a = -q and b = q+8
so -q>0 and q+8>0
solving gives q<0 and q>-8
or -8<q<0
but then you have -q<0 and q+8< 0 so q>0 and q<-8 hmmm