The coordinate of point `P` are `(a,b)` where a is root of the equation `x^(2)+x-42=0` and `b` is integral root of the equation `x^(2)+ax+(a^(2)-37)=0.` The coordinates `P` can be

The roots of the equation ax+(a+b)x-b*=0 are

If (3+i) is a root of the equation x^(2)+ax+b=0 then a is

If p + iq be one of the roots of the equation x^(3) +ax +b=0 ,then 2p is one of the roots of the equation

If a root of the equation ax^(2)+bx+c=0 be reciprocal of a root of the equation a'x^(2)+b'x+c'=0 then

If roots of the equation ax^(2)+2(a+b)x+(a+2b+c)=0 are imaginary then roots of the equation ax^(2)+2bx+c=0 are

The roots of the equation x^(2) + ax + b = 0 are "______" .

If one root is ten xx the other root of the equation 2x^(2)-33x+p=0 then p=

The abscisae of A and B are the roots of the equation x ^(2) + 2ax -b ^(2) =0 and their ordinates are the roots of the equation y ^(2) + 2 py -q ^(2) =0. The equation of the circle with AB as diameter is

x coordinates of two points B and C are the roots of equation x^2 +4x+3=0 and their y coordinates are the roots of equation x^2 -x-6=0 . If x coordinate of B is less than the x coordinate of C and y coordinate of B is greater than the y coordinate of C and coordinates of a third point A be (3, -5) , find the length of the bisector of the interior angle at A.