Question

Which of the following constants can be added to x2 - 3x to form a perfect square trinomial?

Answer 1

9/4=2,25

Answer 2

Thank you so much!

Answer 3

How did you figure it out?

Answer 4

Find the coefficient of the x term
Divide it by 2.
Then square it.

Answer 5

Find the coefficient of the x term: -3

Divide it by 2: \(-\dfrac{3}{2} \)

Then square it: \(\dfrac{9}{4} \)

Answer 6

A perfect square trinomial factors into this form:
\( (x - h)^2 \)
If we expand this form out, we get the perfect square trinomial.
\( x^2 - 2h x + h^2 \)

We may compare the coefficients between these two formats:
\(x^2 = x^2 \)
\( \color{blue}{-2h} x = \color{blue}{-3}x \) ==> 2h = 3 ==> h = 3/2 --> h^2 = (3/2)^2 goes below.
\( \color{blue}{h^2} = \color{blue}{\text{constant added}} \) h^2 = constant
This is where the mechanical process comes from: We always would set -2h ( from the expanded form of x^2 - 2hx + h^2) equal to the linear coefficient, and h^2 is always the constant addition.

The process is taken to be (divide linear coefficient by 2) (square the result to find constant for perfect square)

Answer 7

Thank you so much!! You helped a lot.

Answer 8

you're welcome!