JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(\alpha, \beta, \gamma\) be the real roots of the equation, \(x ^{3}+ ax ^{2}+ bx + c =0,( a , b , c \in R\) and \(a , b \neq 0)\) If the system of equations (in, \(u,v,w\)) 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 solution, then the value of \(\frac{a^{2}}{b}\) is
- A \(5\)
- B \(3\)
- C \(1\)
- D \(0\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
\(\left|\begin{array}{lll}\alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta\end{array}\right|=0\) \(\Rightarrow-(\alpha+\beta+\gamma)\left(\alpha^{2}+\beta^{2}+\gamma^{2}-\sum \alpha \beta\right)=0\) \(\Rightarrow-(-a)\left(a^{2}-2 b-b\right)=0\)…
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