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If one zero of the polynomial (a^2+9)x^2...

If one zero of the polynomial `(a^2+9)x^2+13x+6a` is the reciprocal of the other, find a

A

`a = 5`

B

`a = -3`

C

`a = 2`

D

`a = 3`

Text Solution

Verified by Experts

The correct Answer is:
D
Let one zero of the given polynomial be `alpha`.
Then, the other zero is `1/alpha.`
`:. " product of zeros " = (alpha xx 1/alpha) = 1.`
But, product of zeros = `("constant term")/("coefficient of " x^(2)) = (6a)/((a^(2)+9)).`
`:. (6a)/((a^(2)+9)) = 1 rArr a^(2) + 9 = 6a`
` rArr a^(2) + 9 - 6a = 0`
` rArr (a-3)^(2) = 0`
` rArr a - 3 = 0 rArr a = 3.`
Hence, a = 3.
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