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A quadratic equation whose roots are $\cos e c^{2} θ$ and $\sec^{2} θ$ can be

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x2−2x+2=0

x2−3x+3=0

x2−x+1=0

None of these

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detailed solution

Correct option is D

Sum of roots=sec2θ+cosec2θ=1cos2θ+1sin2θ = 4sin22θ≥4Also, product of roots=sec2θcosec2θ=4sin22θ≥4∴The required quadratic equation will be x2−tx+t=0 where t≥4.

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A quadratic equation whose roots are cosec2θ and sec2θ can be

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A quadratic equation whose roots are $\cos e c^{2} θ$ and $\sec^{2} θ$ can be