Which of the following is not the quadratic equation whose roots are `cos e c^2thetaa n dsec^2theta?` `(a) x^2-6x+6=0` (b) `x^2-7x+7=0` `(c) x^2-4x+4=0` (d) none of these

Options

A. `x^2-6x+6=0`
B. `x^2-7x+7=0`
C. `x^2-4x+4=0`
D. None of these

Answer

D

Explanation

`sec^2theta+cosec^2theta=1/cos^2theta+1/sin^2theta`
`=(cos^2theta+sin^2theta)/(cos^2thetasin^2theta)=sec^2thetacosec^2theta`
Now, `sec^2theta+cosec^2theta=2+tan^2theta+cot^2theta`
`=4+(tantheta-cottheta)^2`
`ge4`
Hence, all equations can have roots `sec^2theta" and " cosec^2theta`.