SOLUTION: What are the values of the constant A in the equation 3(x+4)(x+A)=0

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Question 424888: What are the values of the constant A in the equation 3(x+4)(x+A)=0
Answer by Gogonati(855) About Me  (Show Source):
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Solution:The equation has two roots: X1=-4 and X2=-A, where A>0.
Our equation can be written:3x^2+12x+3Ax+12A=0 => 3x^2+(3A+12)x+12A=0
Using Vi eta's Formula X1+X2=-b/2a and X1*X2=c/a where a=3, b=3A+12 and c=12A :
-4-A=-(3A+12)/6 => 4+A=(1/2)A+2 =>A-A/2=-2 => A/2=-2 => A=-4
-4X2=12A/3 =>-4X2=4A =>X2=-A => X2=-(-4)=4.
Answer: The value of A=-4.