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The equation  has three roots, one of which is the sum of the other two. What is ?

 Aug 30, 2023
 #1
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Call the roots   a , b , a + b

 

By Vieta

 

a + b + a + b  =  -8   

So

2 (a + b) =  -8

a + b =  -4

 

And

ab + a (a + b)  +  b(a + b)   = -4

ab + a (-4) + b (-4)  = -4

ab  - 4(a + b) =  -4

ab - 4(-4)  =  -4

ab + 16  =  -4

ab =  -20

 

And finally

a * b * ( a + b)  =  -c

ab * ( a + b)  = -c

-20 * -4 = -c

80  =  -c

-80 = c

 

P.S ....  the roots are  -2 ± 2sqrt (6)  and  -4

 

 

cool cool cool

 Aug 30, 2023

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