Question

if one of the zeroes of p(x) =(a^2+4)x^2+13x+4a is a reciprocal of other , then find valie of a

Answer 1

if one root is reciprocal of other that means there product is 1
product of root = c/a = 1
4a/(a^2+4) =1
4a = a^2 + 4
a^2 + 4 - 4a =0
(a-2)^2 =0
a = 2
hope it helps.