If one root of the equation `x^2 - px + q = 0`be twice the other, show that `2p^2 = 9q`

If one root of the equation ax^2+ bx+ c=0 be n times the other,show that (n+1)^2/n=b^2/(ac)

If one root of the equation x^2 +px+ 12 = 0 be 4 and if the roots of the equation x^2 + px + q = 0 be equal, find q

If one root of the equation 2x^2-10x+p=0 is 2 then the value of p is

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

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

If p be the ratio of roots of the equation ax^2 + bx + c = 0 , show that (p + 1)^2/p=b^2/(ac) .

If one root of the equation x^2+ax+3=0 is 1,then its other root is a)2 b)-2 c)3 d)-3

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

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