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Heya
_____________________________
Alfa + Beta = -4/k
And
Alfa × Beta = 4/k
=>
Alfa² + Beta² = 24
=>
( Alfa + Beta )² - 2 ( Alfa × Beta ) = 24
=>
16/k² - 2 ( 4/k ) = 24
=>
2/k² - 1/k = 3
=>
2k - k² = 3k³
=>
k = 0 OR 3k² + k - 2 = 0
=>
3k² + 3k - 2k - 2 = 0
=>
3k ( k + 1 ) -2 ( k + 1) = 0
=>
k = -1 OR. k = 2/3
_____________________________
Alfa + Beta = -4/k
And
Alfa × Beta = 4/k
=>
Alfa² + Beta² = 24
=>
( Alfa + Beta )² - 2 ( Alfa × Beta ) = 24
=>
16/k² - 2 ( 4/k ) = 24
=>
2/k² - 1/k = 3
=>
2k - k² = 3k³
=>
k = 0 OR 3k² + k - 2 = 0
=>
3k² + 3k - 2k - 2 = 0
=>
3k ( k + 1 ) -2 ( k + 1) = 0
=>
k = -1 OR. k = 2/3
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