Question

SAT: If a>0 and 16x^2+bx+9=(4x+a)^2 for all values of x, what is the value of b?

Answer 1

i am sure there is a snappy way to do this, but lets use a trick instead

Answer 2

I'm up for anything, haha

Answer 3

ok i thought i had something snappy,but i guess not
lets try this instead, maybe i am being silly
it says true for all \(x\) so we know that if \(x=0\) we get \(9=a^2\) and so \(a=3\) or \(a=-3\)

Answer 4

then
\[16x^2+bx+9=(4x+a)^2=16x^2+8ax+a^2=16x^2+8ax+9\] so our two choices are either \(b=8\times 3=24\) or \(b=-24\)

Answer 5

oooh it says \(a>0\) doh

Answer 6

oh here are the answer choices:
3
8
16
24
72

Sorry for not posting these up!

Answer 7

that means \(a=3\) and so \(b=24\)

Answer 8

choices don't help unless you know how to get them

Answer 9

You're right.
So did you plug a random number in?

Answer 10

i ignored the \(a>0\) part, this means \(a=3\)

Answer 11

no, not random

Answer 12

to solve for \(a\) i chose \(x=0\)

Answer 13

that way the left hand side is 9 and the right hand side is \(a^2\)
then you know \(a=3\)

Answer 14

So to figure out that a=3, you plugged in zero for x? @satellite73

Answer 15

yes