Without expanding a determinant at any stage, show that |`|x^2+x ,x+1 , x+2|,|, 2x^2+3x-1 3x , 3x-3 | , | x^2+2x+3, 2x-1 ,2x-1||=x A+B ,w h e r eAa n dB` are determinant of order 3 not involving `xdot`

Without expanding a determinant at any stage, show that |{:(x^(2)+x, x+1, x+2),(2x^(2) +3x-1, 3x, 3x-3),(x^(2) +2x+3, 2x-1, 2x-1):}|=xA+B where A and B are determinants of order 3 not involving x.

" If " |{:(x^(2)+x,,x+1,,x-2),(2x^(2)+3x-1,,3x,,3x-3),(x^(2)+2x+3,,2x-1,,2x-1):}|=xA +B then

Without expanding at any stage, show that Delta=|{:(x^2+x+2,2x^2+3x+1,3x^2+5x+3),(20x^2+20x+59,40x^2+60x+20,60x^2+100x+70),(2x^2+2x+6,4x^2+6x+2,6x^2+10x+7):}|=x^2A+xB+C , where A and B are determinants of order 3 not involving x….

x ^ (2) + 2x + 3x = 1

If |(x^2+x,x+1,x-2),(2x^2+3x-1,3x,3x-3),(x^2+2x+3,2x-1,2x-1)|=ax-12 then 'a' is equal to (1) 12 (2) 24 (3) -12 (4) -24

y=|(x^2+x, x+1, x-2),(2x^2+3x+1, 3x, 3x-3),(x^2+3x+2, 2x-1, 2x-1)| represents (A) a straight line (B) a circle (C) a parabola (D) none of these

Show that x = 2 is a root of the equation |[x, -6, -1], [2, -3x, x-3], [-3, 2x, 2+x]|=0

Add 2x^2-3x+1 to the sum of 3x^2-2x and 3x+7.

If a,b,c are in A.P .and f(x)=|[x^2+x+a+1, x^2+1, 1] , [2x^2+x+b-1, 2x^2-1, 1] , [3x^2+x+c-2, 3x^2-2, 1]| then f'(x) is

The LCM of the polynomials x^3 +3x^2 +3x + 1, x^2 +2x+1 and x^2 -1 is :