Which of the following constants can be added to x² + x to form a perfect square trinomial?

Solution:

A perfect square trinomial is an expression that can be expressed as a square of a real number.

Given expression: x² + x

To find the perfect square, we need no assign a constant value to this expression, to make this of the form (a + b)².

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

Thus, the constant value 1/2 needs to be added to x² + x, to make it a perfect square trinomial.

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Which of the following constants can be added to x² + x to form a perfect square trinomial?

Summary:

The constant value 1/ 2 needs to be added to x² + x to make it a perfect square