Question:
If one zero of the polynomial (a^2 +9)x^2 +13x+ 6a is the reciprocal of the other find a
Answer:
Given, polynomial is (a2 + 9)x2 + 13x + 6a
Let te zeros of the polynomials are p and 1/p
Now, product of zeros = 6a/(a2 + 9)
=> p * 1/p = 6a/(a2 + 9)
=> 6a/(a2 + 9) = 1
=> a2 + 9 = 6a
=> a2 - 6a + 9 = 0
=> (a - 3)2 = 0
=> a - 3 = 0
=> a = 3
So, the value of a is 3
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