If one of the zeroes of the polynomial (a^2+9)x^2+13x+6a is the reciprocal of the other. Find the value of a
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a = 3 .
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polynomial is (a2+9)x2 + 13x + 6a
Let one zero be b then other zero will be reciprocal of it i.e.1/b.
∴ product of the zeroes = constant term/cofficient of x2 = 1 (as b*1/b = 1)
6a/(a2+9) = 1
⇒ 6a = a2+9
⇒ a2 -6a + 9 = 0
⇒ (a-3)2 = 0
⇒ a - 3 = 0
⇒ a = 3
polynomial will be (32+9)x2 + 13x + 6*3
= 18x2 + 13x + 18
This polynomial will be have imaginary roots because b2-4ac<0
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