Which of the following constants can be added to x2 + x to form a perfect square trinomial?
A perfect square trinomial is an expression that can be expressed as a square of a real number.
Answer: The constant value 1/ 2 needs to be added to x2 + x to make it a perfect square
Go through the steps given below, to understand the derivability of the solution.
Given expression: x2 + x
Let the constant value added be c.
Thus, the expression becomes: x2 + x + c
For a perfect square of the form (a + b)2 , all possible terms are a2 + 2ab + b2
On comparing terms of the perfect square with those of the assumed expression with constant c, we get:
a2 = x2 ⇒ a = x,
b2 = c
2ab = x ⇒ 2xb = x [since a = x]
dividing both the sides by 2x, we get:
b = 1/2
Therefore c = b2 = (1/2)2 = 1/4