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Maths Question Help

Hey guys,
Do you also mind helping me with question 10? I got k>-9 but why must both roots be positive and how do I arrive at k<0? Thank you
(edited 11 months ago)
Reply 1
The roots must be positive because you are doing the quadratic equation to find t^2 which has to be positive,

So 6 - root(36 + 4k) > 0 must hold meaning that k < 0 if you rearrange
Reply 2
Original post by grhas98
The roots must be positive because you are doing the quadratic equation to find t^2 which has to be positive,

So 6 - root(36 + 4k) > 0 must hold meaning that k < 0 if you rearrange


Thanks so much! But where do they get 6-root(36+4k) from?
Reply 3
Original post by Nithu05
Thanks so much! But where do they get 6-root(36+4k) from?


Last line of the frist part, so solving the quadratic
x^2 - 6x - k = 0
The bold is (double) the smallest root which must be positive.
Reply 4
Original post by mqb2766
Last line of the frist part, so solving the quadratic
x^2 - 6x - k = 0
The bold is (double) the smallest root which must be positive.


Just to confirm they used the quadratic formula and set the numerator>0. Is the reason they didn't use the 6+root36+4k because it is already positive as established by the fact that k>-9?
(edited 11 months ago)
Reply 5
Original post by Nithu05
Just to confirm they used the quadratic formula and set the numerator>0. Is the reason they didn't use the 6+root36+4k because it is already positive as established by the fact that k>-9?


The previous root is the smallest one. If thats postiive, then so must be this one
... + sqrt(...)
which is greater than it.
(edited 11 months ago)

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