Question

If x2 + mx + m is a perfect-square trinomial, which equation must be true?

x2 + mx + m = (x – 1)2

x2 + mx + m = (x + 1)2

x2 + mx + m = (x + 2)2

x2 + mx + m = (x + 4)2

Answer 1

Explanation:

x² + mx + m = (x + 2)²

Answer 2

x² + mx + m comparing to ax² + bx + c

a = 1, b = m, c = m.

For perfect square trinomial, b² = 4ac

b² = 4ac

m² = 4*1*m

m² = 4m

m² - 4m = 0

m(m - 4) = 0

m = 0, or m - 4 = 0, m = 4.

Using m = 4,

x² + mx + m = x² + 4x + 4 = (x + 2)²

x² + mx + m = (x + 2)²