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if the equation ax 2 +bx +c=0 and x 2 +2x+4=0 have a common rootand a,b,,c belongs toN then a:b:c ?

if the equation ax2 +bx +c=0 and x2+2x+4=0 have a common rootand a,b,,c belongs toN then a:b:c ?

Grade:11

2 Answers

Ajay
209 Points
7 years ago
Point to note: For a quadratic equation complex roots  are conjugate of each other 
Equation x2+2x+4=0  have complex roots say z1 and z2 and z2 = conjugate(z1)
suppose Z1 is root of ax2 +bx +c=0 then the other root is conjugate(z1) = z2.
This means both equations are essentially same.
Hence a:b:c = 1:2:4
 
Ajay
209 Points
7 years ago
I must correct that in this case both equations are not exactly same but the ratio of coeficients for both equation will be same which will give the same answer.
a:1 = b:2 = c:4

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