If $\alpha $, $\beta $ are roots of the equation $6{x^2} + 11x + 3 = 0$, then
- ${\text{both}}\;{\cos ^{ - 1}}\alpha \;{\text{and}}\;{\cos ^{ - 1}}\beta \;{\text{are}}\;{\text{real}}$
- ${\text{both}}\;\cos {\text{e}}{{\text{c}}^{ - 1}}\alpha \;{\text{and}}\;{\cos ^{ - 1}}\beta \;{\text{are}}\;{\text{real}}$
- ${\text{both}}\;\cos {\text{e}}{{\text{c}}^{ - 1}}\alpha \;{\text{and}}\;{\cot ^{ - 1}}\beta \;{\text{are}}\;{\text{real}}$
- Both $B\ and\ C$
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AI explanation
Factoring the quadratic 6x squared plus 11x plus 3 equals 0 gives the roots alpha equals negative 1/3 and beta equals negative 1/2. The inverse cosecant of negative 1/3 is real, and the inverse cosine of negative 1/2 is real. Furthermore, the inverse cotangent of negative 1/2 is also real. Because the inverse cosecant of alpha is real alongside both the inverse cosine of beta and the inverse cotangent of beta being real, both corresponding statements are true. The result is Both B and C.