Question

Solve 5n^2=35=0 using zero product property or factoring

Answer 1

Pretty please type out all of the instructions when you post a problem. What is your end goal in "solving this problem"? If it's to "solve the following equation," say so.

I have no idea what you mean by "zero product property" and invite you to provide an explanation.

But 5n^2+35 =0 is easily factored into 5(n^2+7); to find the value of n, set n^2+7 = to 0 and solve for n. (Easier said than done, as you'll soon find out. Please explain why.)

Answer 2

Yes, this is for solving I got the answer n=iroot7 But I'm not confident i did it right.

Answer 3

I'd always appreciate your showing your work (not just the answer). I could give you more meaningful feedback if you'd show what you've done. You could use the equation editor or the Draw function below, if you wanted to.

Answer 4

\[5n ^{2}+35=0\]
subtracted 35 from both sides
\[5n ^{2}=-35\]
divided by 5
\[n ^{2}=-7\]
square rooted them
\[n=\sqrt{-7}\]
\[n=i \sqrt{7}\]

Answer 5

Good start. Actually, n= (plus or minius) Sqrt(7). You have TWO imaginary roots.

Answer 6

Because a negative squared number will equal a positive number. Will it be \[\pm i \sqrt{7}\]

Answer 7

Your very last line of type is correct.
Your " a negative squared number will equal a positive number" is, unfortunately, factually incorrect. What were you trying to say?

Answer 8

I think to use the zero product rule, you need to factor the 5 out
5(n^2+7) =0
by the zero product rule, either 5 or n^2+7 is equal to 0, for sure 5 is not, so n^2+7.

I know this seems trivial, but it asked for it:)

Answer 9

\[(-8)^{2}=64 \] but \[-8^{2}=-64\] all i was saying is that i know why it's plus or minus.

Answer 10

I made n^2+7 equal to zero and got the same answer. I was just unsure what to do with the 5 that i factored so i tried a different method. I think I understand now.

Answer 11

its all about this property, say we want to solve ab=7
there are infinite solutions to this equation
examples: a = 7, b=1, a = 42 b = 1/6, a = 21 b = 1/3

so this does not help much, but if we have something like this
ab=0
we can claim for sure that at least one of the factors, a or b, is equal to 0
(try to think of two numbers that are not 0, but multiply to 0)

in your situation, you had 5n^2+36=0
now there are two ways to do this problem
5n^2+35 = 0 becomes 5n^2=-35, divide the 5, 2^2 = -7 then .......
or
factor our the 5(n^2+7) = 0, now we use the zero product rule because since 5 is not equal to 0, we know that n^2+7 = 0 (if ab=0 and a is not 0 , then b is 0)
then we go one to solve n^2 = -7......

now this is sort of a bad way of showing this property, because the method in which you used to solve this, does not "show" that you are actually using the zero product property. It is a little more involved than this situation warrants, but without the zero product property rule, you would not have been able to "cancel" the five when you went from 5n^2=-35 to n^2 = -7.