can the quodriatic polynomial x^2+kx+k have equal zeroes for some odd interger k>1 ?
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soln: Since roots are equal, hence D must be zero.
i.e D = 0
or, b^2 - 4ac = 0
Here a = 1, b = k & c = k
=> k^2 - 4 × 1 × k = 0
=> k^2 -4k = 0
=> k(k - 4) = 0
either k = 0, or k = 4
Since according to question statement k must be odd & k > 1.
our above solution i.e k = 0(< 1) or k = 4(> 1 but it is not odd) doesn't satisfy given condition.
so given polynomial doesn't have equal zeros for some odd integer greater than 1.
Hope it helps you !
i.e D = 0
or, b^2 - 4ac = 0
Here a = 1, b = k & c = k
=> k^2 - 4 × 1 × k = 0
=> k^2 -4k = 0
=> k(k - 4) = 0
either k = 0, or k = 4
Since according to question statement k must be odd & k > 1.
our above solution i.e k = 0(< 1) or k = 4(> 1 but it is not odd) doesn't satisfy given condition.
so given polynomial doesn't have equal zeros for some odd integer greater than 1.
Hope it helps you !
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