If 1 is a common root of the equations `ay^2+ay+3=0` and `y^2+y+b=0`,then find the value of ab.

If x=1 is a common root of the equations a x^2+a x+3=0 and x^2+x+b=0 , then a b=

If the equation x^(2) - 3x + b = 0 and x^(3) - 4x^(2) + qx = 0 , where b ne 0, q ne 0 have one common root and the second equation has two equal roots, then find the value of (q + b) .

Find the roots of given equation 2y ^2−y−1=0

If line 3x-ay-1=0 is parallel to the line (a+2)x-y+3=0 then find the values of a.

The abscissa 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) + 2py -q^(2) = 0. The equation of the circle with AB as diameter is

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

The abscissae of two points A and B are the roots of the equaiton x^2 + 2x-a^2 =0 and the ordinats are the roots of the equaiton y^2 + 4y-b^2 =0 . Find the equation of the circle with AB as its diameter. Also find the coordinates of the centre and the length of the radius of the circle.

If the equations x^2+ax+b=0 and x^2+bx+a=0 have one common root. Then find the numerical value of a+b.

The common tangent to the parabola y^2=4ax and x^2=4ay is

Let the equation of the plane containing line x-y-z-4=0=x+y+2z-4 and parallel to the line of intersection of the planes 2x+3y+z=1 and x+3y+2z=2 be x+Ay+Bz+C=0 . Then the values of |A+B+C-4| is …..