QJEEM19Ma4c66: JEE Main 2019 Mathematics - Class 12 JEEM19Ma4c66 Solution: The sum of the real roots of the equation

Question

Verified Solution • 2025–26 Session moderate

The sum of the real roots of the equation

| \begin{matrix} x & - 6 & - 1 \\ 2 & - 3 x & x - 3 \\ - 3 & 2 x & x + 2 \end{matrix} | = 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

∴

sum of roots = 0

Step-by-Step Verified Solution