The least value of |$a|$ for which $ an heta$ and cot $ heta$ are roots of the equation $x^{2} + ax + 1 = 0$, is

Question

The least value of |$a|$ for which $	an	heta$ and cot $	heta$ are roots of the equation $x^{2} + ax + 1 = 0$, is

Dr. Abubacker · Accepted Answer

(a)
Given equation $x^{2} + ax + 1 = 0.$
Since, roots are $	an{	heta\ and\cot	heta.}$
$	herefore\$ Product of roots, $	an{	heta\  \bullet \cot	heta} = a\  \Rightarrow a = 1$
Again, since roots are real.
$	herefore a^{2} - 4 \geq 0\  \Rightarrow |a| \geq 2$
Thus, the least value of $|a|$ is 2.

Q. The least value of |$a|$ for which $\tan\theta$ and cot $\theta$ are roots of the equation $x^{2} + ax + 1 = 0$, is

Explanation

Reviewed by Dr. Abubacker

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