Question

The quadratic equation whose roots are $\tan 22{\frac{1}{2}}^{\circ }$ and $\cot 22{\frac{1}{2}}^{\circ }$ is

• A. $x^2-2\sqrt{2}x+1=0$
• B. $x^2+2\sqrt{2}x+1=0$
• C. $x^2+2\sqrt{2}x-1=0$
• D. $2x^2+2\sqrt{2}x+1=0$

Answer 1

The correct option is A $x^2-2\sqrt{2}x+1=0$

We know that
$\tan \frac{\pi }{8}=\tan 22{\frac{1}{2}}^{\circ }=\sqrt{2}-1\cot \frac{\pi }{8}=\cot 22{\frac{1}{2}}^{\circ }=\sqrt{2}+1$
Sum of roots $=2\sqrt{2}$
Product of roots $=1$
Hence quadratic equation is $x^2-2\sqrt{2}x+1=0$