If the value of real number a>0 for which x²-5 a x+1=0 and x²-a x-5=0 have a common real root is 3/(√(2 β)) then β is equal to _ _ _ _ _ _.

Complex Numbers and Quadratic Equations: JEE Main 2023 Mathematics question

JEE Main 2023 · 30 Jan, Evening shift · Q45

JEE Main 202330 Jan, Evening shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

If the value of real number

a>0

for which

x^2-5 a x+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 ___________.

Your answerType your answer. Integers and decimals are accepted.