If a, b,c are in G.P. and `ax^2 + 2bx + c = 0` and `px^2 + 2qx + r = 0` have common roots then verify that `pb^2 - 2qba + ra^2 = 0`

The lines ax + by + c = 0, where 3a + 2b + 4c= 0, are concurrent at the point

If y= e^(ax) sin(bx), show that y2 - 2ay1 + ( a^2 + b^2 ) y = 0

If a,b,c,d are in G.P., then prove that: (b-c)^2 + (c-a)^2+(d-b)^2=(a-d)^2

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

If the sum of the roots of the quadratic equation ax^2+bx+c=0 is equal to the sum of the squares of their reciprocals,then prove that 2a^2c=c^2b+b^2a .

A quadratic equation ax^2 + bx + c = 0 , with distinct coefficients is formed. If a, b, c are chosen from the numbers 2, 3, 5, then the probability that the equation has real root is

The abscissae 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

If tan A & tan B are the roots of the quadratic equation x^2 - ax + b = 0 , then the value of sin^2 (A +B) is: