Find-the-number-of-solution-s-of-x-2-x-sin-x-0-x-0-pi-

Question Number 14470 by Tinkutara last updated on 01/Jun/17

Find the number of solution (s) of

x^{2} + x + \sin x = 0, x \in [0, π]

Commented by mrW1 last updated on 01/Jun/17

s i n c e x \in [0, π]

x^{2} ⩾ 0

x ⩾ 0

\sin x ⩾ 0

x^{2} + x + \sin x ⩾ 0

“ =^{″} o n l y a t x = 0

\Rightarrow x^{2} + x + \sin x = 0 h a s o n l y

o n e s o l u t i o n x = 0

Commented by Tinkutara last updated on 01/Jun/17

But minimum value of x^{2} + x is \frac{- 1}{4} at

x = \frac{- 1}{2} . Will it not affect the answer ?

Commented by mrW1 last updated on 01/Jun/17

x \in [0, π]

s o x ⩾ 0, a n d t h e r e i s n o m i n i m u m .

Commented by Tinkutara last updated on 01/Jun/17

Thanks Sir!