# perfect square of trinomials

• Feb 1st 2008, 06:18 AM
starrynight
perfect square of trinomials
The question is:
Which of the following polynomials is NOT a perfect square trinomial?
A) x2 + 2x + 1
B) 4x2 - 4x + 1
C) x2 + 3x + 9
D) 16x2 + 8x + 1
E) all of them are perfect square trinomials

the way it is explained in my lesson is very confusing. I am very confused. please help me! :confused:
• Feb 1st 2008, 06:41 AM
topsquark
Quote:

Originally Posted by starrynight
The question is:
Which of the following polynomials is NOT a perfect square trinomial?
A) x2 + 2x + 1
B) 4x2 - 4x + 1
C) x2 + 3x + 9
D) 16x2 + 8x + 1
E) all of them are perfect square trinomials

the way it is explained in my lesson is very confusing. I am very confused. please help me! :confused:

Look at the quadratic formula for a moment:
$\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Now, if the discriminant (the $\displaystyle b^2 - 4ac$) is equal to 0 then then you are adding $\displaystyle \pm 0$ to the -b in the numerator. Thus the two roots of the quadratic will be the same, ie. the quadratic is a perfect square.

So for which of these is the discriminant equal to 0?

-Dan
• Feb 1st 2008, 07:37 AM
starrynight
I think the answer is x2 + 3x + 9. Am I right?
• Feb 1st 2008, 07:39 AM
topsquark
Quote:

Originally Posted by starrynight
I think the answer is x2 + 3x + 9. Am I right?

Well, as the rest give a discriminant of 0 and this one has a discriminant of $\displaystyle 9 - 4 \cdot 9 = -27 \neq 0$, I'd say "yes." :)

-Dan