Question

If the equation $|sinx{|}^2+|sinx|+b=0$ has two distinct roots in $[0,\pi ]$, then the number of integers in the range of b is/are equal to

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is C

2

$si{n}^x\theta co{s}^x\theta \ge 1,0<\theta <\frac{\pi }{2}$

$\text{we know,}si{n}^2\theta +co{s}^2\theta =1$

$In[O,\frac{\pi }{2}]⟶sin\&cos\text{both are +ve}.$

$Ifx>2;si{n}^x\theta +co{s}^2+co{s}^x\theta \le 1$

$(\because sin\&cos\le 1-\text{fractional})$

$Ifx<2;si{n}^2\theta +co{s}^2\theta \ge 1$

$\therefore si{n}^x\theta co{s}^x\theta \ge 1whenx\le 2$

$xϵ(-\infty ,2]$