Grade 11Algebra
find the integer k for which the inequality x^2 – 2(4k-1)x + 15k^2 – 2k – 7 > 0 is valid for any x
find the integer k for which the inequality x^2 – 2(4k-1)x + 15k^2 – 2k – 7 > 0 is valid for any x
1 Answer
Ajay
The inequality will be greater than zero if D is less than zero
4(4k-1)2 – 4(15k2 – 2k – 7) less than zero
Simplifying this we get
K2-6k+8 less than zero
(k-4)(k-2) less than zero
K lies in (2, 4)
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