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If alpha,beta(alpha < beta) are the root...

If `alpha,beta(alpha < beta)` are the roots of equation `6x^2+11="" x+3="0` , then which following real? (a) `cos^(-1)alpha` (b) `sin^(-1)beta` (c) `cosec^(-1)alpha` (d) both `cot^(-1)alpha` and `cot^(-1)beta`

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To solve the problem step by step, we need to find the roots of the quadratic equation given and then check the validity of the inverse trigonometric functions for those roots. ### Step 1: Find the roots of the quadratic equation The given equation is: \[ 6x^2 + 11x + 3 = 0 \] We can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] ...
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