what is the point of factoring this?

Question

y^2-24y+144=0

its (y-12)(y-12) right?

but now what do i do to get the value(s) of y ?

Answer 1

Whenever you have an equation where a factorization product equals zero, at least one of the factors must themselves be zero. That fact enables you to solve the original quadratic or higher order equation.

Thus (x - a)(x - b) = 0 means that

EITHER (x - a) = 0, OR (x - b) = 0.

(If both parentheses were non-zero, their product couldn't be zero. THAT's why you know that at least one of them must be zero.)

That being so, EITHER x = a (making the first parenthesis above zero), OR x = b (making the second one zero).

[Note that this "Either ... or" formulation is very important. With a and b generally different, it is simply wrong to say "therefore x = a and x = b," although you'll often see that done on YA!]

In your case, you have (y - 12)(y - 12) = 0.

In that case, there is a "repeated" or "double" root of y = 12, meaning that if you were to plot the function x = (y - 12)(y - 12) it would look like a parabola lying on its side with a VERTICAL TANGENT at the point (x, y) = (0, 12). Tangency of the curve or function to a line parallel to one of the axes is the hallmark of a function or graph with a "double root" at that point.

Live long and prosper.

Answer 2

Or, (y - 12)^2 = 0 => y = 12

Answer 3

Hi,
Good! You factored correctly. You have:
(y-12)(y-12) = 0 (Same as the trinomial, just factored.)
Now, there's a technique called the zero factor theorem that says, or maybe just implies, that to find the values of x, set each factor equal to zero and solve for x . Let' do it.
First factor:
y-12 = 0
y = 12

Same thing for the other factor:
y-12 = 0
y = 12
So, the values of x are the same. In the language of math, that's called having a multiplicity of 2.

Hope this helps.
FE

Answer 4

You're not finished. What you have is
(y - 12)(y-12) =0 (The =0 is important)
How can you have two nos. a, and b multiplied together giving you 0? Either one could be zero (which in this case they are the same y - 12)
So y - 12 = 0 and y = 12.
If a and b were different then set each one to zero,

Answer 5

once you have factored it

(y-12)(y-12)=0

you set both sides equal to zero (because anything multiplied by zero is zero)

and then you have

y-12=0 and y-12=0
(most of the time these will not be the same)

you would solve for both and get

y=12 and y=12

so your answer is

y=12

(if you had twp diffrent answers, lets say y=6 and y=12 you would say your answer is y=6,12 meaning that it is equal to both)

after this you can put 12 in to the problem in place of y and solve....if you get 0 you did it right....

Answer 6

The answer you gave is correct, you can also write it as (y-12)^2 or y = 12.

What you found are the roots of the equation. In science and Engineering they are value to know for a host of applications.

Answer 7

You know that (y-12) has to equal zero for the whole thing to be zero, so y has to equal 12.