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Question

The entire graphs of the equation y=x2+kxāˆ’x+9 is strictly above the x-axis if and only if


A

k<7

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B

-5<k<7

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C

k>-5

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D

-7<k<5

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Solution

The correct option is B

-5<k<7


y=x2+(k1)x+9=(x+k+12)2+9(k12)2
For entire graph to be above x-axis, we should have
9(x12)2 > 0
k22k35<0(k7)(k+5) < 0

i.e., -5<k<7


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