If one root of (a² + 9)x² + beta x + 6a is the reciprocal of other. Find the value of
a.
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Answer:
a = 3
Step-by-step explanation:
The product of the roots is equal to the constant coefficient divided by the coefficient of x². Since the roots are reciprocals, their product is 1. Therefore
6a / ( a² + 9 ) = 1
=> a² + 9 = 6a
=> a² - 6a + 9 = 0
=> ( a - 3 )² = 0
=> a = 3
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