If alpha and beta are the roots of the equati | vedclass

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(A) Given the quadratic equation $6x^2 - 5x + 1 = 0$.By comparing with $ax^2 + bx + c = 0$,we have $a = 6, b = -5, c = 1$.The sum of roots $\alpha + \

Vedclass · Accepted Answer

$\pi / 4$

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(A) Given the quadratic equation $6x^2 - 5x + 1 = 0$.By comparing with $ax^2 + bx + c = 0$,we have $a = 6, b = -5, c = 1$.The sum of roots $\alpha + \beta = -b/a = 5/6$.The product of roots $\alpha \beta = c/a = 1/6$.Using the formula $	an^{-1}\alpha + 	an^{-1}\beta = 	an^{-1}\left(\frac{\alpha + \beta}{1 - \alpha \beta}ight)$,Substitute the values: $	an^{-1}\left(\frac{5/6}{1 - 1/6}ight) = 	an^{-1}\left(\frac{5/6}{5/6}ight) = 	an^{-1}(1)$.Since $	an^{-1}(1) = \pi / 4$,the final value is $\pi / 4$.

If $\alpha$ and $\beta$ are the roots of the equation $6x^2 - 5x + 1 = 0$,then the value of $\tan^{-1}\alpha + \tan^{-1}\beta$ is:

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