If one zero of the polynomial (a^2+2)x^2 +10x +3a) is the reciprocal of the other. find a

Given that:

one zero of the polynomial (a^2+2)x^2 +10x +3a is the reciprocal of the other.

We need to find a

Let one zero be α
Then other zero=1/α

product of zeroes=c/a

α x 1/ α=c/a

Then from the equation we get,

1= 3a/ a2 + 2

a2 + 2= 3a

a2 – 3a + 2= 0

a2 – a – 2a + 2=0

a(a-1)-2(a-1)=0

(a-1) (a-2)=0

a=1 and a=2

Therefore the values of a are a=1 and a=2

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