Question

If the point $(0,\lambda )$ is a point of the region bounded by the semicircle $x=\sqrt{9-y^2}$ and the line $x=0$ then equation $x^2-2x-\lambda =0$

• A. at least one real root in $[2,3]$
• B. at least one real root in $[-1,0]$
• C. two real roots in $[-1,3]$
• D. no real roots in $(0,2)$

Answer 1

Answer: (C)

two real roots in $[-1,3]$

Putting $(0,\lambda )$ in the given semi circle $\lambda =\pm 3$
Now corresponding to $\lambda =-3$ there is no real roots of the given quadratic.
And corresponding to $\lambda =3$ roots are $-1,3$