Is the following statement True or False? Justify your answer.The only

1.	Is the following statement 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.
Answer» 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.

Is the following statement 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.

Answer»

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.