Question

Find the value of $\alpha$ for which point $(\alpha ,2\alpha +1)$ doesn't lie outside the parabola $y=x^2+x+1$.

Answer 1

Solution :-

If a point lies inside the curve s

Then $S_1$ should be Less then o

$S_1$ Now

$2a+1-a^2-a-1<0$

$a^2-a>0$

$a(a-1)>0$

So. a belongs to $(1,\infty )$ and $(-\infty ,0)$

$aϵ(1,\infty )\cup (-\infty ,0)$