PhysChemTutor's answer to help's Secondary 3 A Maths Singapore question.
i counter checked already... it had to be -3 < m <2.
then it is x^2 + 6.
Explain My last two steps?
then it is x^2 + 6.
Explain My last two steps?
You had not learned this method of solving inequality? using number line...
cause for part a) i got (m+3)(m-2)>0
so since its >0 i put
positive x positive >0
m+3>0 and m-2>0
m>-3 and m>2
or
negative x negative >0
m+3<0 and m-2<0
m<-3 and m<2
so since its >0 i put
positive x positive >0
m+3>0 and m-2>0
m>-3 and m>2
or
negative x negative >0
m+3<0 and m-2<0
m<-3 and m<2
in the first place, why greater than 0? discriminant should be less than zero... Let us sort this out first before I tell you how to solve the inequality
oh its less than 0
wait why isit less than 0 how do you know if its all positive
wait why isit less than 0 how do you know if its all positive
read my solution x^2 - 2mx - m + 6 > 0
Do you get this?
Do you get this?
yeah
how do you know if your discriminant is less or more than 0?
so if eqn is >0 D is < 0?
so if my eqn is <0 D is > 0??
so if eqn is >0 D is < 0?
so if my eqn is <0 D is > 0??
Then the discriminant should be less than 0. D less tham 0 means the quadratic never meet the x axis.
ohhh okay thank you i get it now
discriminat > 0 means the curve cuts x-axis at two points. D = 0 means the curve touches the x-axis once. D <0 means the curve never meet the x-axis.....
the expression now always greater than 0 means it never meet the x-axis... means D < 0.
You slowly think...
the expression now always greater than 0 means it never meet the x-axis... means D < 0.
You slowly think...
so for eg when the eqn is >0 it means it did not cut x axis so discriminant is < 0
while when eqn <0 it means it cuts x axis so discriminant is > 0
while when eqn <0 it means it cuts x axis so discriminant is > 0
expression less than zero, it also never cuts the x-axis,,,,, D is still < 0
but if eqn <0 it cuts x axis?
expression > 0 or < 0 , both cases also the curve never meet the x-axis. .... Because the x-axis is the f(x) = 0 line. > 0 or < 0 ..... both also never = 0
so only an eqn = 0 then can d >0 or = 0 and have point(s) of intersection
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