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# Discriminant. watch

1. The question is:
Find an inequality for K in its simplest form such that the quadratic equation
Kx^2-(2K+3)x+(K+2)=0 has 2 distinct solutions.

K>9/4

But the real solution is
K>-9/4

Can someone please explain how the minus for the K is cancelled out but for -9/4 it isn't?
2. (Original post by Aksa09)
The question is:
Find an inequality for K in its simplest form such that the quadratic equation
Kx^2-(2K+3)x+(K+2)=0 has 2 distinct solutions.

K>9/4

But the real solution is
K>-9/4

Can someone please explain how the minus for the K is cancelled out but for -9/4 it isn't?
does it have 2 distinct solution? i did this

b²-4ac
(2k+3)²-4*k*(k+2)>0
(4k²+12k+9)-4k(k+2)>0
4k²+12k+9-4k²-8k>0
4k+9>0
4k>-9
k>-9/4
3. (Original post by Aksa09)
The question is:
Find an inequality for K in its simplest form such that the quadratic equation
Kx^2-(2K+3)x+(K+2)=0 has 2 distinct solutions.

K>9/4

But the real solution is
K>-9/4

Can someone please explain how the minus for the K is cancelled out but for -9/4 it isn't?
I'm sorry, which minus sign are you referring to, if you post some working I can try to spot a mistake.
4. (Original post by thefatone)
does it have 2 distinct solution? i did this

b²-4ac
(2k+3)²-4*k*(k+2)>0
(4k²+12k+9)-4k(k+2)>0
4k²+12k+9-4k²-8k>0
4k+9>0
4k>-9
k>-9/4
Thankyou.
But I thought the value for B would be -2K+3 as the equation has a minus before it.
5. (Original post by Aksa09)
Thankyou.
But I thought the value for B would be -2K+3 as the equation has a minus before it.
B is -(2k+3), or -2k-3, but not -2k+3. Then when you square a negative number, you can just square the positive (e.g. (-3)^2 = 3^2 = 9), so you can do (2k+3)^2 as it's simpler than (-2k-3)^2.
6. (Original post by HapaxOromenon)
B is -(2k+3), or -2k-3, but not -2k+3. Then when you square a negative number, you can just square the positive (e.g. (-3)^2 = 3^2 = 9), so you can do (2k+3)^2 as it's simpler than (-2k-3)^2.
Oh yes, got it. Thankyou so much

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