Ack Discriminant Probs (1 Viewer)

[Seraph]

Hey ppl having a bit of trouble with these discriminants in quadratic equations

heres one im having particular probs with

Find all values of k for which kx^2 + 3kx + 6 is positive definite

now when they say positive definite does that mean i take it as b^2-4ac > 0 ?????? Someone told me you take it as < 0 , i tried that , did not get a correct answer and it did not make much sense to me since it has to be a positive definite

Oh and another question say i get a solution a > 3 or a > -3 how do i graph that in one line like 3<a<3 ... i dont get how to do this? and i also dont understand how these are read , for example -8<k<8 , how would u read that as? i would say -8 is less than k and 8 is less than k , but i know that is not right....

help me out plz

 

[crazylilmonkee]

positive def means a>0 and b^2-4ac <0
cos there isnt a root, but its concave up

 

[Seraph]

what so do you mean like this

b2-4ac < 0

(3k)^2 - 4(k * 6) < 0

6k^2 -24k < 0
6k(k-4) < 0

k < 0 or k < 4

????????? , the answer says 0 < k < 2 and 2/3 ( i think it says that its a bit faded)

 

[crazylilmonkee]

first mistake
b^2 = (3k)^2 = 9k^2
so.. discriminant = 9k^2-24k <0
3k(3k-8)<0
which means 0 < k < 8/3

 

[Seraph]

UGHHHHHHHHHHHHHHHHHh






hah thx

 

[crazylilmonkee]

no probs
damn that didnt show.. didnt know i had to leave spaces