Multiple choice

A root of the equation $17x^2+17x\tan\left(\displaystyle 2\tan^{-1}\frac{1}{5}-\frac{\pi}{4}\right)-10=0$ is?

  1. $\displaystyle\frac{10}{17}$
  2. $\displaystyle -1$
  3. $\displaystyle -\frac{7}{17}$
  4. $\displaystyle 1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let theta = 2*tan^-1(1/5) - pi/4. tan(theta) = tan(2*tan^-1(1/5) - pi/4). tan(2*tan^-1(1/5)) = (2*(1/5)) / (1-(1/25)) = (2/5) / (24/25) = 5/12. tan(theta) = (5/12 - 1) / (1 + 5/12) = (-7/12) / (17/12) = -7/17. Equation: 17x^2 + 17x(-7/17) - 10 = 0 => 17x^2 - 7x - 10 = 0. Roots: (17x+10)(x-1) = 0. x=1 or x=-10/17.

Keep practicing — related questions