Question

How do I use the zero product property to solve this equation? -16t^2 + 28t + 8 = 0

Answer 1

@mathmate

Answer 2

Zero product property means that
if a*b = 0, then either a=0, b=0, or both equal to zero.
When applied to factoring, say \(f(x)=x^2-3x+2=0\)
Since \(f(x)=x^2-3x+2=(x-2)(x-1)\) which is a product of (x-2) and (x-1), then
(x-2)=0, (x-1)=0, or both.
This allows us to say x-2=0 means x=2, or x-1=0 means x=1.
Therefore the solution to f(x)=0 is x=2 or x=1.

You can now apply a similar procedure to the given problem in question.

Answer 3

So does that mean I have to factor the problem first to be able to find t?

Answer 4

@mathmate

Answer 5

Yes, factoring would be the first step, once you know what to do afterwards.

Answer 6

Do not forget to take out common factors of ALL the terms before attempting more elaborate factoring.
Example: factor 2x^2-6x+4 = 2(x^2-3x+2)=2(x-2)(x-1)

Answer 7

I factored it to this now: -4(t - 2)(4t + 1) = 0
So, now I have to set each factor equal to 0, and solve for t, right?

Answer 8

Exactly! (all factors except -4, of course!)

Answer 9

Yes, ok, then

-4(t-2)=0
-4t-8=0
-4t-8+8=0+8
-4t=8
-4t/4=8/4
t=2

-4(2-2)=0

Answer 10

OR

(4t + 1) = 0
4t + 1 = 0
4t + 1 - 1 = 0 - 1
4t = -1
4t/4 = -1/4
t = -1/4

Answer 11

Correct?

Answer 12

Sorry I have ignored you for the last 8 minutes because I was helping someone else in the mean time!

Perfect! Everything is correct and well done.

Answer 13

Thanks! :)

Answer 14

You're welcome! :)