Q.

If the quadratic equation ax2 + bx+ c = 0 (a > 0) has sec2⁡θ and cosec2⁡θ as its roots, then which of the following must hold good?

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a

b + c = 0

b

b2−4ac≥0

c

c≥4a

d

4a+b≥0

answer is A.

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Detailed Solution

sec2⁡θ+cosec2⁡θ=sec2⁡θ⋅cosec2⁡θSum of the roots is equal to their product and the roots are real. Hence,−ba=caor b + c = 0Also b2−4ac≥0or   c2−4ac≥0or   c(c−4a)≥0or   c−4a≥0               (∵ c>0)Furtherb2+4ab≥0or   b+4a≤0     (∵ b<0)
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