if one zero of polynomial (a2 +9)x2 +13x +6a is reciprocal of other find value of a

x = {-13 ±(169 - 4(6a)(a²+9))}/(2(a²+9))

x = {-13 ±(169 - 24a³ - 216a)}/(2(a²+9))

Since the zeros i.e. x1 and x2 are reciprocals,

{-13 +(169 - 24a³ - 216a)}/(2(a²+9)) = (2(a²+9))/{-13 -(169 - 24a³ - 216a)}

(-13)² - (169 - 24a³ - 216a) = (2(a²+9))²

24a(a² + 9) = 4(a²+9)²

24a = 4(a²+9)

4a² -24a+36 = 0

a² - 6a + 9 = 0

a = 3

Regards,

Team,

TopperLearning.