Question

Find the value of n such that x^2-19x n is a perfect square trinomial.

Answer choices:
A. -19/2
B. 361/4
C. 361
D. 361/2

Answer 1

B. 361/4
you get: x^2-19x+361/4=(x-19/2)^2

Answer 2

Answer: The correct option is (b)
`(361)/(4).`

Step-by-step explanation: We are given to select the correct value of 'n' such that
`x^2-19x+n` becomes a perfect square trinomial.

The standard form of a perfect square trinomial is

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

Now, we can write

`x^2-19x+n\\\\=x^2-2* x* (19)/(2)+(361)/(4)+n-(361)/(4)\\\\\\=(x-(19)/(2))^2+n-(361)/(4).`

So, for the given expression to be perfect trinomial,

`n-(361)/(4)=0\\\\\Rightarrow n=(361)/(4).`

Thus, (b) is the correct option.