MCQ
The system of equations $\lambda x + y + z = 0,$ $ - x + \lambda y + z = 0,$ $ - x - y + \lambda z = 0$, will have a non zero solution if real values of $\lambda $ are given by
- ✓$0$
- B$1$
- C$3$
- D$\sqrt 3 $
Therefore $\lambda = 0$, since $\lambda = i\sqrt 3 $ does not exist.
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$P(x) = 2x^3 + x^2 + 3x - 2? $
$(i)$ It has exactly one positive real root.
$(ii)$ It has either one or three negative roots.
$(iii)$It has a root between $0$ and $1.$
$(iv)$ It must have exactly two real roots.
$(v)$ It has a negative root between $- 2$ and $-1.$
$(vi)$ It has no complex roots.