If the equation x2+4 x sin θ+ tan θ=0 (0

Question

If the equation x2+4 x sin θ+ tan θ=0 (0 < θ < (π/2)) has repeated roots, then θ equals (A) (π/12) (B) (π/6) (C) (π/12) or (5 π/12) (D) (π/6) or (π/12)

Tardigrade Admin · Accepted Answer

D =0 ⇒ 16 sin 2 θ=4 tan θ ⇒ 4 sin 2 θ= tan θ ⇒ 2 sin 2 θ=1 sin 2 θ=(1/2) ⇒ 2 θ=(π/6) or (5 π/6) ⇒ θ=(π/12) or (5 π/12)

Q. If the equation $x^{2} + 4 x sin θ + tan θ = 0$ $(0 < θ < \frac{π}{2})$ has repeated roots, then $θ$ equals

$\frac{π}{12}$

$\frac{π}{6}$

$\frac{π}{12}$ or $\frac{5 π}{12}$

$\frac{π}{6}$ or $\frac{π}{12}$

$D = 0 \Rightarrow 16 sin^{2} θ = 4 tan θ$
$\Rightarrow 4 sin^{2} θ = tan θ$
$\Rightarrow 2 sin 2 θ = 1$
$sin 2 θ = \frac{1}{2}$
$\Rightarrow 2 θ = \frac{π}{6}$ or $\frac{5 π}{6}$
$\Rightarrow θ = \frac{π}{12}$ or $\frac{5 π}{12}$

Q. If the equation x2+4xsinθ+tanθ=0 (0<θ<2π​) has repeated roots, then θ equals

12π​

6π​

12π​ or 125π​

6π​ or 12π​