CGGO Q23

0. The entire graph of the function f(x) = x² + kx - x + 9 is strictly above the x-axis if and only if

Answer
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Option : D
Explanation :
y = x² + (k- 1) x + 9 = (x + (k -1)/2)² - ((k- 1)/2) + 9
For the entire graph to lie above the x-axis. y should be greater than 0, for all x.
So, 9 - ((k- 1)/2) 2 > 0 i.e., (k - 7) (k + 5) < 0 or - 5 < k < 7

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