find the range of values of k , such that f(x) = kx^2 + 2(k+1)x + (9k+4)/x^2 -8x + 17 is always negative
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Answer:
Step-by-step explanation:
Solution :-
(k - 2)x² + 2(2k - 3)x + (5k - 6) are real and equal.
Here, a = k - 2, b = 4k - 6, c = 5k - 6
D = b² - 4ac
= (4k - 6)²- 4 × (k - 2)(5k - 6)
= 16k² + 36 - 48k - 20k² + 64k - 48
= 4k² - 16k + 12
= k² - 4k + 3 = 0
= (k - 3)(k - 1) = 0
= k = 3, 1
Nature of roots of a quadratic equation:-
(i). If b² - 4ac > 0, the quadratic equation has two distinct real roots.
(ii). If b² - 4ac = 0, the quadratic equation has two equal real roots.
(iii). If b² - 4ac < 0, the quadratic equation has no real roots.
4.8
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