The number of points in (- , ) for which x^ 2 -x - =0, is : - Vidyadip

MCQ

The number of points in $(-\infty,\infty)$ for which $\text{x}^{2}-\text{x}\sin\text{x}-\cos\text{x}=0,$ is :

A
$6$
B
$4$
✓
$2$
D
None of the above

✓

Answer

Correct option: C.

$2$

Better approch is with graphs. Considering graphs in eqaution we get
$\text{x}^{2}-\text{x}\sin\text{x}-\cos\text{x}=0$
$\text{x}^{2}=\text{x}\sin\text{x}+\cos\text{x}$
Let $\text{f}(\text{x})=\text{x}^{2},\text{g}(\text{x})=\text{x}\sin\text{x}+\cos\text{x}$
Using graphical methods,we can do the graph of $f(x)$ and $g(x)$
The graph $f(x)$ and $g(x)$ intersects at two points between $(-\infty,\infty)$

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