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State whether the following statement is true or false.

For some odd integer $k > 1,$ the quadratic polynomial $x 2 + k x + k$ could have equal zeroes.

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True

False

answer is B.

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Detailed Solution

The given quadratic polynomial is,

p (x) = x 2 + k x + k

For equal zeroes, we have,

b 2 − 4 a c = 0

⇒ k 2 − 41 k = 0 ⇒ k 2 − 4 k = 0 ⇒ k = 0 & k = 4

Since the values of

k

are 0 and 4 which are even numbers. Therefore, there doesn’t exist any value of

k

such that the quadratic polynomial

x 2 + k x + k

has equal zeroes for some odd integer

k > 1.

Thus, the given statement is not true.
Hence option (2) is correct.

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