Solve the equation `|[a-x, c, b], [ c, b-x, a], [b, a, c-x]|=0` where `a+b+c!=0.`

If a+b+c=0, one root of [[a-x, c, b],[c, b-x, a],[ b, a, c-x]]=0 is a. x=1 b. x=2 c. x=a^2+b^2+c^2 d. x=0

Solve the following determinant equation: |[x+a, b, c], [c, x+b, a], [a ,b, x+c]|=0

The product of all values of t , for which the system of equations (a-t)x+b y+c z=0,b x+(c-t)y+a z=0,c x+a y+(b-t)z=0 has non-trivial solution, is (a) |[a, -c, -b], [-c, b, -a], [-b, -a, c]| (b) |[a, b, c], [b, c, a], [c, a, b]| (c) |[a, c, b], [b, a, c], [c, b, a]| (d) |[a, a+b, b+c], [b, b+c, c+a], [c, c+a, a+b]|

Solve the equation |{:(x+a,x+b,x+c),(x+b,x+c,x+a),(x+c,x+a,x+b):}|=0

If a ,b ,c in R , then find the number of real roots of the equation Delta =|[x, c,-b],[-c, x, a], [b,-a,x]|=0

if a+b+c=0 then Delta=|{:(a-x,c,b),(c,b-x,a),(b,a,c-x):}|=0 is

Find the number of real root of the equation |[0,x-a, x-b],[ x+a,0,x-c],[ x+b, x+c,0]|=0,a!=b!=c and b(a+c)> a c

If a , b , c , are roots of the equation x^3+p x+q=0, prove that |[a ,b, c],[ b ,c, a],[ c, a, b]|=0

In a triangle A B C ,/_C=pi/2dot If tan(A/2)a n dtan(B/2) are the roots of the equation a x^2+b x+c=0,(a!=0), then the value of (a+b)/c (where a , b , c , are sides of opposite to angles A , B , C , respectively) is

If a,b and c are the roots of the equation x^3+2x^2+1=0 , find |[a,b,c],[b,c,a],[c,a,b]| .