JEE MAIN - Mathematics (2019 - 10th April Evening Slot - No. 18)
The sum of the real roots of the equation
$$\left| {\matrix{ x & { - 6} & { - 1} \cr 2 & { - 3x} & {x - 3} \cr { - 3} & {2x} & {x + 2} \cr } } \right| = 0$$, is equal to :
$$\left| {\matrix{ x & { - 6} & { - 1} \cr 2 & { - 3x} & {x - 3} \cr { - 3} & {2x} & {x + 2} \cr } } \right| = 0$$, is equal to :
- 4
0
1
6
Explanation
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
$$ \Rightarrow $$ – 5x3 + 30x –30 + 5x = 0
$$ \Rightarrow $$ x3 – 7x + 6 = 0
$$ \therefore $$ sum of roots = 0
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