TS EAMCET · Maths · Quadratic Equation
If \(x_1, x_2, x_3\) are the real roots of the equation \(x^3-x^2 \tan \theta+x \tan ^2 \theta+\tan \theta=0\) and \(0 < \theta < \frac{\pi}{4}\), then the value of \(\tan ^{-1} x_1+\tan ^{-1} x_2+\tan ^{-1} x_3\) at \(\theta=\frac{\pi}{12}\) is
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi}{3}\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{6}\)
Step-by-step Solution
Detailed explanation
According to given informations, \(\begin{aligned} & x_1+x_2+x_3=\tan \theta \\ & x_1 x_2+x_2 x_3+x_3 x_4=\tan ^2 \theta \\ & \text { and } \quad x_1 x_2 x_3=-\tan \theta \\ & \text { So, } \tan ^{-1} x_1+\tan ^{-1} x_2+\tan ^{-1} x_3\end{aligned}\)…
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