Question

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

Answer 1

Answer: The correct option is (b)
`(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* x* (1)/(2)+(1)/(4)+b-(1)/(4)\\\\\\=(x-(1)/(2))^2+b-(1)/(4).`

So, for the given expression to be perfect trinomial,

`b-(1)/(4)=0\\\\\Rightarrow b=(1)/(4).`

Thus, (b) is the correct option.

Answer 2

x2 - x + 1/4
x2 - x + 1/4 becomes (x-1/2)2
it becomes perfect square so the correct answer for the above is
B that is 1/4
hope it helps