Question

If the equation $\lambda x^2-2x+3=0$ has positive roots for some real $\lambda$, then

• A. $\lambda >0$
• B. $\lambda >\frac{1}{3}$
• C. $0<\lambda \le \frac{1}{3}$
• D. $\lambda \le \frac{1}{3}$

Answer 1

The correct option is C $0<\lambda \le \frac{1}{3}$

Sum and product of roots should be $>0\Rightarrow \lambda >0$
Roots should be real so$\lambda \le 1/3$
Combining both we get $\lambda \in (0,1/3]$