Matrix involving roots

A question is this type if and only if it involves a matrix whose entries contain roots of a polynomial and asks about properties like singularity or determinant.

1 questions · Standard +0.8

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CAIE FP1 2011 November Q3

7 marks Standard +0.8

3 The equation $$x ^ { 3 } + 5 x ^ { 2 } - 3 x - 15 = 0$$ has roots \(\alpha , \beta , \gamma\). Find the value of \(\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 }\). Hence show that the matrix \(\left( \begin{array} { c c c } 1 & \alpha & \beta \\ \alpha & 1 & \gamma \\ \beta & \gamma & 1 \end{array} \right)\) is singular.