### NotATutor's answer to hehe'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...

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

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

so if eqn is >0 D is < 0?

so if my eqn is <0 D is > 0??

ohhh okay thank you i get it now

the expression now always greater than 0 means it never meet the x-axis... means D < 0.

You slowly think...

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?

so only an eqn = 0 then can d >0 or = 0 and have point(s) of intersection