Let α, β, γ be the real roots of the equation, x³ + ax² + bx + c = 0, (a, b, c R and a, b ≠ 0). If the system of equations (in u, v, w) given by α u + β v + γ w = 0, β u + γ v + α w = 0; γ u + α v + β w = 0 has non-trivial solution, then the value of (a²)/b is

Matrices and Determinants: JEE Main 2021 Mathematics question

JEE Main 2021 · 18 Mar, Morning shift · Q4592

JEE Main 202118 Mar, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

Let

\alpha

\beta

\gamma

be the real roots of the equation, x³ + ax² + bx + c = 0, (a, b, c

\in

R and a, b

\ne

0). If the system of equations (in u, v, w) given by

\alpha

u +

\beta

v +

\gamma

w = 0,

\beta

u +

\gamma

v +

\alpha

w = 0;

\gamma

u +

\alpha

v +

\beta

w = 0 has non-trivial solution, then the value of

{{{a^2}} \over b}