First slide

Theory of equations

Question

If $α, β, γ$ are the roots of the equation $x^{3} + x + 1 = 0,$ then the value of $α^{3} β^{3} γ^{3}$

Moderate

A

0
B

$- 3$
C

$3$
D

$- 1$

Solution

We know that the roots of the equation
${ax}^{3} + {bx}^{2} + cx + d = 0$ follows $αβγ = - d / a$
Comparing above equation with given equation
we get $d = 1, a = 1$
So, $αβγ = - 1 or α^{3} β^{3} γ^{3} = - 1$ .

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