First slide

Introduction to Determinants

Question

If $α, β, γ$ are the roots of ${px}^{3} + {qx}^{2} + r = 0$ , then the value of the determinant $|\begin{array}{lll} αβ βγ γα \\ βγ γα αβ \\ γα αβ βγ \end{array}|$ is

Moderate

A

p
B

q
C

0
D

r

Solution

Operation $C_{1} \to C_{1} + C_{2} + C_{3}$ gives
$(αβ + βγ + γα) |\begin{array}{ccc} 1 & βγ & γα \\ 1 & γα & αβ \\ 1 & αβ & βγ \end{array}|$
From the given equation, $αβ + βγ + γα = 0$ . So, the value of determinant is 0.

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