|[a,b,ax+by],[b,c,bx+cy],[ax+by,bx+cy,0]|

If a gt 0 and discriminant of ax^(2) + 2bx + c is negative, then Delta = |(a,b,ax +b),(b,c,bx +c),(ax +b,bx +c,0)| , is

[[a, b, ax + byb, c, bx + cyax + by, bx + cy, 0]] = (b ^ (2) -ac) (ax ^ (2) + 2bxy + cy ^ (2))

det[[ Prove that: ,b,ax+bya,c,bx+cyax+by,bx+cy,0]]=(b^(2)-ac)(ax^(2)+2bxy+cy^(2))

If |{:(a,b,ax+b),(b,c,bx+c),(ax+b,bx+c,0):}|'=0 then "a,b,c are in" .. (''where ax^2+2bx-c ne' 0)

If a gt 0 and discriminant of ax^(2)+2bx+c=0 is negative, then the value of - |(a,b,ax+b),(b, c,bx+c),(ax+b,bx+c,0)| is -

If a gt 0 and discriminant of ax^2+2bx+c is negative, then : Delta=|(a,b,ax+b),(b,c,bx+c),(ax+b,bx+c,0)| is :

The non-zero roots of the equation Delta =|(a,b,ax+b),(b,c,bx+c),(ax+b,bx+c,c)|=0 are

The non-zero roots of the equation Delta=|(a,b,ax+b),(b,c,bx+c),(ax+b,bx+c,c)|=0 are

The determinant Delta=|(a,b,ax+b),(b,c,bx+c),(ax+b,bx+c,c)| is equal to zero, if a)a,b,c are in A.P. b)a,b,c are in G.P. c)a,b,c are in H.P. d) ax^(2) + bx + c = 0