Can the quadratic polynomial x2 + kx + k have equal zeroes for s

1.	Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1? Justify your answer.
Answer» 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.

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

Answer»

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.