Mathematics: Which of the following constants can be added to x2 - x to form a perfect square trinomial? a)1/2 b)1/4 c) 1

Which of the following constants can be added to

ciarrap552

03.01.2022

The correct option is (b) $\dfrac{1}{4}.$

Step-by-step explanation: We are given to select the correct constant that can added to x^2-x , so thet it becomes a perfect square trinomial.

A perfect square trinomial is of the following form:

(x+a)^2=x^2+2a+a^2.

Let the constant to be added be 'b'. Then, we can write

$x^2-x+b\\\\=x^2-2\times x\times \dfrac{1}{2}+\dfrac{1}{4}+b-\dfrac{1}{4}\\\\\\=(x-\dfrac{1}{2})^2+b-\dfrac{1}{4}.$

So, for the given expression to be perfect trinomial,

$b-\dfrac{1}{4}=0\\\\\Rightarrow b=\dfrac{1}{4}.$

Thus, (b) is the correct option.

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