Q.
If the quadratic equation ax2 + bx+ c = 0 (a > 0) has sec2θ and cosec2θ 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
sec2θ+cosec2θ=sec2θ⋅cosec2θSum 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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