Question

Can the quadratic polynomial x² + kx + k have equal zeroes for some odd integer k > 1?

Answer 1

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.