Show that the roots of the equation `x^2 -2px + p^2 - q^2 + 2qr-r^2 = 0` are rational.

The roots of the equation x+2y=4 and 2y-x=0 are

The roots of the equation x+2y=4 and 2x-y=0 are

The roots of the equation ax^2+x+b=0 are equal if

If the roots of the equation 3x^2 +2 (p + q+ r)x + (pq + qr + pr) = 0 are equal show that p=q=r .

Find the roots of the following equations: 2x^2+1/2=2x

If 2 is a root of the equation x^2+px-8 = 0 and the equation x^2 + px + q = 0 has equal roots, find p, q .

If -3 is a root of the equation x^2+ px + 6 = 0 and the equation x^2 +px +q = 0 has equal roots, find p,q .

If alpha , beta be the roots of the equation x^2-px+q=0 ,form the quadratic equation whose roots are 2alpha-beta , 2beta-alpha

If a , b , c , are rational and a + b + c= 0 . Show that the roots of the following equation are rational. ax^2 + bx + c = 0 .

If the roots of the equation ax^2 + bx + c = 0 are in the ratio 2:3 , then prove that 6b^2 = 25ac