If one zero of the polynomial p(x) =(a^2+9)x^2+45x+6a,is the reciprocal of the other,find the value of a.
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Let α and β be the zeros of the polynomial (a²+9)x²+45+6a
It is given that α=1/β
αβ=1
c/a=1
constant term/coefficient of x²=1
6a/a²+9=1
6a=a²+9
a²-6a+9=0
a²-3a-3a+9=0
a(a-3)-3(a-3)=0
(a-3)(a-3)=0
a=3
It is given that α=1/β
αβ=1
c/a=1
constant term/coefficient of x²=1
6a/a²+9=1
6a=a²+9
a²-6a+9=0
a²-3a-3a+9=0
a(a-3)-3(a-3)=0
(a-3)(a-3)=0
a=3
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