`ax+by=c` and `mx+ny=d`. If `an ne bm`, then these simultaneous equations have

If D_(x)=-18 and D = 3 are values of determinant for certain simultaneous equation in x and y then value of x is .........

Let a , b , c and m in R^(+) . The possible value of m (independent of a , b and c ) for which atleast one of the following equations have real roots is {:(ax^(2)+bx+cm=0),(bx^(2)+cx+am=0),(cx^(2)+ax+bm=0):}}

The equations x^2 +3x+5=0 and ax^2+bx+c=0 have a common root. If a,b,c in N then the least possible values of a+b+c is equal to

Write D_(x) for the following simultaneous equations . 5x+2y=10,-3x+y=-11

Let alpha ,beta and gamma be the roots of the equations x^(3) +ax^(2)+bx+ c=0,(a ne 0) . If the system of equations alphax + betay+gammaz=0 beta x +gamma y+ alphaz =0 and gamma x =alpha y + betaz =0 has non-trivial solution then

If a,b and c are distinct positive real numbers in A.P, then the roots of the equation ax^(2)+2bx+c=0 are

If the equation x^2 + bx + ca = 0 and x^2 + cx + ab = 0 have a common root and b ne c , then prove that their roots will satisfy the equation x^2 + ax + bc = 0 .

Let a,b, c and d be non-zero numbers. If the point of intersection of the lines 4ax + 2ay+c=0 and 5bx+2by +d=0 lies in the fourth quadrant and is equidistant from the two axes, then