Roots (1 Viewer)

[nrlwinner]

I have a question and I'm not sure how to solve it.

Show that the roots of the equation

4(m+1)x^2 -4(m-1)x -3 = 0 (m does not equal -1)

are real for all m.



P.S. Can you take the discriminate of a discriminate?

 

[study-freak]

 

[lolokay]

P.S. Can you take the discriminant of a discriminant?

why wouldn't you be able to?

 

[Lukybear]

Wouldnt it be possible to not complete the square and just state the conclusion??

 

[hermand]

Wouldnt it be possible to not complete the square and just state the conclusion??

i think so yeah, because even if m is negative, m^2 is greater than m when m is greater than one, less than negative one, and when it's between 1 & -1, the addition of four will cancel any negative out anyway.

 

[Timothy.Siu]

i think so yeah, because even if m is negative, m^2 is greater than m when m is greater than one, less than negative one, and when it's between 1 & -1, the addition of four will cancel any negative out anyway.

but u have to show that.
how can u be so sure

 

[hermand]

but u have to show that.
how can u be so sure

because it is.

 

[Lukybear]

but u have to show that.
how can u be so sure

OO... I get it. By completing the square, its saying that it cant be negative. I c...

 

[study-freak]

because it is.

HSC markers will probably not pay you full marks for that though.

 

[lolokay]

if m<-1, then m^2 > -m -> m^2 + m > 0 so m^2 + m + 4 > 0
if -1 < m < 0, then 0 < m^2 < 1
so m^2 + m + 4 > 3
and if m > 0, m^2 > 0
m^2 + m > 0,
as m^2 + m + 4 is greater than zero for each case it is always postive

works well for seeing it intuitively, but as for actually proving you're best to either complete the square or take the disciminant

 

[Lukybear]

How would you take the discriminant lolokay?

 

[lolokay]

if b^2 - 4ac < 0, (and a > 0) the quadratic is always positive
for m^2 + m + 4, the discriminant is 1 - 16 = -15 < 0
so always positive

 

[study-freak]

shouldn't you say that coefficient of x^2>0 to get the mark if you use the discriminant method?

 

[lolokay]

yeah probably would need to

 

[Lukybear]

Ah, I see. Thats very simple concepts applied. Very very good. Hopefully one day ill reach you levels of thinking.

 

[gella]

dammit, wrong thread

 

[gurmies]

dammit, wrong thread

Bahaha, +1 !

 

[dux&src]

Bahaha, +1 !

same for me

 

[omniscience]

roots? niceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

 

[Lukybear]

If thread dosent mind me asking, where was this question from? Which text book?