Question

If one zero of p (x)=ax^2+12x+b is a reciprocal of the other, show that a=b

Answer 1

let it be c
then other 1/c

x+c=0
x =  -c

now putting x = -c 

p(-c)= c^2a +12c+b

now x+1/c=0

x =  -1/c

putting x = -1/c

so we get 1\c^2 +12c+b


now equating both 

c^2a +12c+b=1\c^2 +12c+b

c^2a = 1\c^2

so proved a=b

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