Question

~~Fanning ALL who helps plus Medal~~
Which polynomial is a perfect square trinomial?

49x^2 − 28x + 16

4a^2 − 20a + 25

25b^2 − 20b − 16

16x^2 − 24x − 9

Answer 1

second equation

Answer 2

Are you sure?

Answer 3

yes...

Answer 4

Okay Thank you and the reason why I questioned you is because I looked up the answer and one person said it was A the other said it was D Loll thanks

Answer 5

Hey want to know how to find out?

Answer 6

Sure why not I used to know this so well about 5 months ago

Answer 7

\[
49x^2 − 28x + 16

\]
Take the middle term \(-28\) and then divide by two times the first term \(2\times 49\), then square it:\[
\left(\frac{-28}{2\times 49}\right)^2=\left(-\frac{2}{7}\right)^2=\frac {4}{14}
\]This must be equatl to the last term. Since \(16\neq 4/14\), this one isn't a perfect square.

Answer 8

ahuh

Answer 9

Wait that formula is a bit wrong

Answer 10

Okay go ahead

Answer 11

You have to multiply the first term back i

Answer 12

OK

Answer 13

so which one is the right answer?

Answer 14

A much more intuitive approach is to try to complete the square.

Answer 15

OK

Answer 16

http://www.mathsisfun.com/algebra/completing-square.html

Answer 17

How'd they get d? in the link you showed me just now?

Answer 18

They said \[
d=\frac{b}{2a}
\]

Answer 19

Oh

Answer 20

You want \(e=0\) to have a perfect square which means :\[
c = \frac{b^2}{4a}
\]By the way \[
\frac{b^2}{4a}=a\left(\frac{b}{2a}\right)^2
\]

Answer 21

Okay

Answer 22

Okay let's try it again ok? \[
49x^2 − 28x + 16
\]So \[
\frac{b^2}{4a}=\frac{(-28)^2}{4(49)} = 4\neq 16
\]

Answer 23

Now with \[
4a^2 − 20a + 25

\]We use \[
\frac{b^2}{4a}=\frac{(-20)^2}{4(4)}=\frac{400}{16}=25=c
\]So it is a complete square.

Answer 24

I'm listening

Answer 25

Do you understand how I put b and a into the equation?

Answer 26

hm... what i did was take a times sqrt of c and see if that's the same number as b

Answer 27

I understand and I see penguin

Answer 28

yes yes yes...

Answer 29

Loll

Answer 30

You did \[
a\sqrt c = b
\]? penguin?

Answer 31

yeah, but negative

Answer 32

Well, \[
b^2=4ac
\]Would work, or even \[
b=\sqrt{4ac}
\]But not \[
a\sqrt c = b
\]...

Answer 33

oh okay

Answer 34

@wio so the aswer is a?

Answer 35

The second one happens to be correct.

Answer 36

Ok thank you both