If x^2+3x+5=0 and a x^2+b x+c=0 have com...

If `x^2+3x+5=0` and `a x^2+b x+c=0` have common root/roots and `a ,b ,c in N ,` then find the minimum value of `a+b+c` .

`3`

`9`

`6`

`12`

Text Solution

Verified by Experts

The correct Answer is:

`:'` Roots of the equation `x^(3)+3x+5=0` are non real.
Thus, given equations will have two common roots.
`impliesa/1=b/3=c/5=lamda`[say]
`:.a+b+c=9lamda`
Thus, minimum value of `a+b+c=9 [:' a,b,c epsilonN]`

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