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Question
Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?
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Solution
A Quadratic Equation will have equal roots if it satisfies the condition:
b2 – 4ac = 0
Given equation is x2 + kx + k = 0
a = 1, b = k, x = k
Substituting in the equation we get,
k2 – 4(1)(k) = 0
k2 – 4k = 0
k(k – 4) = 0
k = 0, k = 4
But in the question, it is given that k is greater than 1.
Hence the value of k is 4 if the equation has common roots.
Hence if the value of k = 4, then the equation (x2 + kx + k) will have equal roots.
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