Question

If the value of real number a> 0 for which $x^2$-5ax+1-0 and $x^2-a x-5-0$ have a common real root is $\frac{3}{\sqrt{2 \beta}}$ then $\beta$ is equal to_______

Answer 1

Two equations have common root
∴(4a)(26a)=(−6)2=36
⇒a2=269​
∴a=26​3​
⇒β=13
So, the correct answer is 13.