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The number of real values of ‘t’ such that the system of homogeneous equations $t x + (t + 1) y + (t - 1) z = 0$ , $(t + 1) x + t y + (t + 2) z = 0$ , $(t - 1) x + (t + 2) y + t z = 0$ has non-trivial solution is

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Correct option is C

The condition for a homogeneous system to have a non-trivial solution is Δ=0⇒tt+1t-11-13-111=0⇒t-1-3-(t+1)1+3+(t-1)1-1=0⇒-4t-4t-4=0⇒-8t=4⇒t=-12

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The number of real values of ‘t’ such that the system of homogeneous equations tx+t+1y+t−1z=0,t+1x+ty+t+2z=0,t−1x+t+2y+tz=0 has non-trivial solution is

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The number of real values of ‘t’ such that the system of homogeneous equations $t x + (t + 1) y + (t - 1) z = 0$ , $(t + 1) x + t y + (t + 2) z = 0$ , $(t - 1) x + (t + 2) y + t z = 0$ has non-trivial solution is