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If the quadratic equation whole roots are $\cos e c^{2} θ, s e c^{2} θ$ is $x^{2} - λ x + λ = 0$ then

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λ>4

λ<4

λ≥4

λ≤4

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detailed solution

Correct option is C

sum of the roots =λ=sec2θ+csc2θ=1cos2θ+1sin2θ =sin2θ+cos2θsin2θcos2θ =1sin2θcos2θ =4sin22θ≥4Also product of the roots= csc2θ·sec2θ=1sin2θcos2θ≥4∴The required equation is x2−tx+t=0 where t≥4

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If the quadratic equation whole roots are cosec2θ, sec2θ is x2-λx+λ=0 then

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Ready to Test Your Skills?

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If the quadratic equation whole roots are $\cos e c^{2} θ, s e c^{2} θ$ is $x^{2} - λ x + λ = 0$ then