The sum of the real roots of the equation [| pmatrix x & - 6 & - 1 2 & - 3x & x - 3 - 3 & …

Question

The sum of the real roots of the equation

$$\left| {\begin{pmatrix} x & { - 6} & { - 1}  \
   2 & { - 3x} & {x - 3}  \
   { - 3} & {2x} & {x + 2}  \ \end{pmatrix} } \right| = 0$$, is equal to :

Accepted Answer

x(-3x $$ \times $$ (x + 2) - 2x(x - 3)) + (-- 6) (2(x + 2) + 3 (x -- 3)) + (--1) (4x + 3 (--3x))

$$ \Rightarrow $$ -- 5x3 + 30x --30 + 5x = 0

$$ \Rightarrow $$ x3 -- 7x + 6 = 0

$$ \therefore $$ sum of roots = 0

Solutions · 1