If the value of real number a0 for which x^2-5 ax+1=0 and x^2- ax-5=0 have a common real roots is 3 2 then is equal to .

Question

If the value of real number a>0 for which x^2-5 ax+1=0 and x^2- ax-5=0 have a common real roots is 3 2 then is equal to .

Accepted Answer

Correct answer: 13. (13) Two equations have common root ∴ (4a ) (26a )=(-6)^2=36 ⇒a^2= 926 ∴a= 3 26 ⇒ =13

$If the value of real number a > 0 for which x^{2} - 5 ax + 1 = 0 and x^{2} - ax - 5 = 0 have a common real roots is \frac{3}{2 β} then β is equal to .$