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If one zero of the polynomial (a^2-9)x^2 + 13x + 6a is the rec

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If one zero of the polynomial $(a^{2} - 9) x^{2} + 13 x + 6 a$ is the reciprocal of the other, then the value of $a$ is

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If one zero of the polynomial

(a^{2} - 9) x^{2} + 13 x + 6 a

is the reciprocal of the other, then the value of

a

9 mins ago

Discuss this question LIVE

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Text solutionVerified

We know that equation $a x^{2} + b x + c = 0$

Then sum of roots $= \frac{- b}{a}$ and product of roots $= \frac{c}{a}$

Let the other zero be

α

Therefore, the other zero is

\frac{1}{α}

Now,

α \times \frac{1}{α} = \frac{6 a}{a ^{2} - 9}

=> 1 = \frac{6 a}{a ^{2} - 9}

=> a^{2} + 9 - 6 a = 0

=> a^{2} - 6 a + 9 = 0

=> a^{2} - 3 a - 3 a + 9 = 0

=> a (a - 3) - 3 (a - 3) = 0

=> (a - 3) (a - 3) = 0

=> a = 3

and

a = 3

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Question Text	If one zero of the polynomial $(a^{2} - 9) x^{2} + 13 x + 6 a$ is the reciprocal of the other, then the value of $a$ is
Answer Type	Text solution:1
Upvotes	151