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Question

The value(s) of 'p' for which the parabola represented by quadratic function y=(p2)x2+8x+(p+4) will remain below X-axis for all real values of x is .

A
p(,6)(4,)
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B
p (, 6)
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C
p (4, )
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D
p(6,4)
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Solution

The correct option is B p (, 6)
For a parabola to remain below X-axis, it means the parabola will be downward facing and will not intersect/touch X-axis.
a<op2<0p<2 ...(i) and D<0(8)24(p2)(p+4)<016p24p+2p+8<0p22p+24<0p2+2p24>0(p+6)(p4)>0 ...(ii)From (i) and (ii), we getp<6

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