Question

Does anyone understand the zero product principle for quadric equations?

Answer 1

\[2m ^{2} + 10m=-12\]

Answer 2

factorize the eq. then equate both to zero. you will get the two roots

Answer 3

Well it goes like this
First rearrange the eqn as follows:
\[2m ^{2} + 10m + 12 = 0\]

Answer 4

or the formula for fractions verse the equations without fractions would help. I have the information mixed up--the (x+a)(x+b)=0 is all that is stated

Answer 5

Now the product of the coefficient of m^2 and the constant terms +12 is 24
We have to find factors p and q of 24 so that
pq = 24
and
p + q = 10

Answer 6

Can you give me the value of p and q ??

Answer 7

???????

Answer 8

6 and 4

Answer 9

would you happen to know the formulas?

Answer 10

Absolutely correct !!!!
Ok If we take p as 6 and q as 4
pq = 6 x 4 = 24 and
6+ 4 = 10

So, now we can rewrite the equation as \[2m ^{2} + 6m + 4m + 24 = 0\]

Answer 11

I'm solving it step by step for u

Answer 12

Sorry, I made a mistake with the last eqn !!!
It will be \[2m ^{2} + 6m + 4m + 12 = 0\]

Answer 13

Now we take out common factors as follows:
\[2m(m + 3) +4(m + 3) = 0\]

Answer 14

Now (m + 3) is common and so we can rewrite as follows:
\[(m + 3) (2m + 4) = 0\]

Answer 15

Got it till here????

Answer 16

Now according to the zero product principal, a x b = 0 if either a=0 or b=0

So (m+3)(2m+4) = 0 means that either m+3 = 0 ie. m = -3
or 2m +4 = 0 ie 2m = -4 ie m = -4/2 ie m = -2

Answer 17

Hope it is clear now???