Which Quadratic?
Algebra
Level
3
If both the roots of the quadratic equation are less than 5, then lies in which interval
( 5, 6 ]
[ 4,5 ]
( - ∞ , 4 )
( 6, ∞ )
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1 solution
firstly,
b^2 - 4ac >= 0
4k^2 - 4k^2 + 20 - 4k >=0
k <= 5
now for second part,
2k +- 2*root of (5 - k) / 2
k +- root (5 - k) < 5
(5 - k)^2 > 5 - k
k^2 - 9k + 20 > 0
(k - 4)(k - 5) > 0
k is ( -infinity , 4) union (5 , infinity)
Taking intersection ,
(-infinity, 4)