Question

The sum of the real roots of the equation
`|{:(x, -6, -1), (2, -3x, x-3), (-3, 2x, x+2):}| = 0,` is equal to

Answer 1

Correct Answer - A
Given equation
`|{:(x, -6, -1), (2, -3x, x-3), (-3, 2x, x+2):}| = 0`
On expansion of determinant along R, we get
`x[(-3x)(x+2)-2x (x-3)] + 6[2(x+2)+3(x-3)]-1[9(2x)-(-3x)(-3)]=0`
`rArr x[-3x^(2)-6x-2x^(2)+6x] + 6[2x +4 + 3x-9]-1[4x-9x]=0`
`rArr x(-5x^(2))+6(5x-5)-1(-5x)=0`
`rArr -5x^(3) + 30x-30+5x = 0`
`rArr 5x^(3)-35x + 30 = 0 rArr x^(3) - 7x + 6 =0.`
Since all roots are real
`therefore "Sum of roots " = -("coefficient of "x^(2))/("coefficient of "x^(3)) = 0`