anonymous
  • anonymous
Does anyone understand the zero product principle for quadric equations?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[2m ^{2} + 10m=-12\]
anonymous
  • anonymous
factorize the eq. then equate both to zero. you will get the two roots
anonymous
  • anonymous
Well it goes like this First rearrange the eqn as follows: \[2m ^{2} + 10m + 12 = 0\]

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anonymous
  • anonymous
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
anonymous
  • anonymous
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
anonymous
  • anonymous
Can you give me the value of p and q ??
anonymous
  • anonymous
???????
anonymous
  • anonymous
6 and 4
anonymous
  • anonymous
would you happen to know the formulas?
anonymous
  • anonymous
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 \[2m ^{2} + 6m + 4m + 24 = 0\]
anonymous
  • anonymous
I'm solving it step by step for u
anonymous
  • anonymous
Sorry, I made a mistake with the last eqn !!! It will be \[2m ^{2} + 6m + 4m + 12 = 0\]
anonymous
  • anonymous
Now we take out common factors as follows: \[2m(m + 3) +4(m + 3) = 0\]
anonymous
  • anonymous
Now (m + 3) is common and so we can rewrite as follows: \[(m + 3) (2m + 4) = 0\]
anonymous
  • anonymous
Got it till here????
anonymous
  • anonymous
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
anonymous
  • anonymous
Hope it is clear now???

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