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find k if zeroes of polynomial Kx2-6x+9 are equal

Let the zeroes = a and b
a + b = -(-6)/k
-2a = - 6/k
-a = 6/2 k
a(a) = 9 / k
-k = 9/a2
-k = 9/(2k/6)2

-k = 9/4k2 / 36
-k = k2
-k 2 / k = 1
therefore k = 1


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