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

The only value of k for which the quadratic polynomial kx2 + x + k has equal zeroes is 1/2


The only value of k for which the quadratic polynomial kx2 + x + k has equal zeroes is 1/2: False.

A quadratic polynomial kx2 + x + k have equal roots when its discriminate is equal to


i.e. D = 0


b2 - 4ac = 0


b2 = 4ac


12 = 4(k) (k)


1 = 4k2


k2 = 1/4


k = 1/2


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


2
1