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Question

# Consider the system of equations:x+y+z=0αx+βy+γz=0α2x+β2y+γ2z=0Then the system of equations has

A
A unique solution for all values α,β,γ
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B
Infinite number of solutions if any two of α,β,γ are equal
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C
A unique solution if α,β,γ are distinct
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D
More than one, but finite number of solutions depending on values of α,β,γ
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Solution

## The correct options are B Infinite number of solutions if any two of α,β,γ are equal C A unique solution if α,β,γ are distinctx+y+z=0αx+βy+γz=0α2x+β2y+γ2z=0△=∣∣ ∣ ∣∣111αβγα2β2γ2∣∣ ∣ ∣∣If any of the two values (α,β) or (α,γ) or (β,γ) are equal then △=0Infinite solution Option BFor all different values of α,β,γ△≠0Unique solution Option C

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