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If the equation x^(2)+2x+3=0 and ax^(2)+...

If the equation `x^(2)+2x+3=0 and ax^(2)+bx+c=0, a,b,c in R` have a common root, then `a:b:c` is

A

`1:2:3`

B

`3:2:1`

C

`1:3:2`

D

`3:1:2`

Text Solution

AI Generated Solution

To solve the problem, we need to find the ratio \( a:b:c \) given that the equations \( x^2 + 2x + 3 = 0 \) and \( ax^2 + bx + c = 0 \) have a common root. ### Step 1: Identify the roots of the first equation The first equation is: \[ x^2 + 2x + 3 = 0 \] To find the roots, we can use the quadratic formula: ...
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