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If one zero of polynomial ( …

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If one zero of polynomial ( a square +9) x square +13x 6a is reciprocal of the other, then find the value of a
  • 1 answers

Sia ? 5 years, 10 months ago

Let α and 1α be the zeros of (a+ 9)x+ 13x + 6a.
Then, we have
α×1α=6aa2+9
⇒ 1 = 6aa2+9
⇒ a2 + 9 = 6a
⇒ a2 - 6a + 9 = 0
⇒ a2 - 3a - 3a + 9 = 0
⇒ a(a - 3)  - 3(a - 3) = 0
⇒ (a - 3) (a - 3) = 0
⇒ (a - 3)= 0
⇒ a - 3 = 0
⇒ a = 3
So, the value of a in given polynomial is 3.

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