1. Tardigrade
  2. Question
  3. Mathematics
  4. Let α, β, γ are the real roots of the equation x3+a x2+b x+c=0(a, b, c ∈ R and a ≠ 0). If the system of equations (in u, v and w ) given by α u+β v+γ w=0 ; β u+γ v+α w=0 ; γ u+α v+β w=0 has non-trivial solutions, then a 2 equals

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Q. Let $\alpha, \beta, \gamma$ are the real roots of the equation $x^3+a x^2+b x+c=0(a, b, c \in R$ and $a \neq 0)$. If the system of equations (in $u, v$ and $w$ ) given by $\alpha u+\beta v+\gamma w=0 ; \beta u+\gamma v+\alpha w=0 ; \gamma u+\alpha v+\beta w=0$ has non-trivial solutions, then $a ^2$ equals

Determinants

Solution:

Correct answer is (c) $3 b$