Are the following statements ‘true’ or ‘False’? Justify your answer.

The only value of k for which the quadratic polynomial kx^{2} + x + k has equal zeroes is 1/2

The only value of k for which the quadratic polynomial kx^{2} + x + k has equal zeroes is 1/2: **False.**

A quadratic polynomial kx^{2} + x + k have equal roots when its discriminate is equal to

i.e. D = 0

b^{2} - 4ac = 0

b^{2} = 4ac

1^{2} = 4(k) (k)

1 = 4k^{2}

k^{2} = 1/4

k = 1/2

Hence, k = 1/2 is not the only value for which the polynomial has equal roots.

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