Q8 of 90 Page 2

If one zero of the polynomial (α2 + 9) x2 + 13x + 6α is reciprocal of the other, find the value of a.

Let one zero of the given polynomial is


According to the given condition,


The other zero of the polynomial is


We have,


Product of zeroes,



⇒ α2 – 6α + 9 = 0


⇒ α2 – 3α – 3α + 9 = 0


⇒ α(α – 3) – 3(α – 3) = 0


⇒(α – 3)(α – 3) = 0


⇒(α – 3) = 0 & (α – 3) = 0


⇒ α = 3, 3


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