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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` .

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Roots of `x^(2) + 3x + 5 = 0 ` are non- real.
Thus, given equation will have two common roots.
`rArr (a)/(1) = (b)/(3) = (c)/(5) = lambda`
`rArr a + b + c = 9 lambda, a, b, c in` N
Thus, minimum value of a + b + c is 9.
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