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 alpha , beta be the roots of the equation ax^2 + bx + c = 0 , form the quadratic equation whose roots are 1/alpha , 1/beta

if alpha , beta be the roots of the equation x^2 + x + 1 = 0 , find the quadratic equation whose roots are alpha^2000 and beta^2000

Find the quadratic equation whose roots are given as -4 and 1/2 .

If alpha , beta are the zeroes of the polynomial x^2-3x+ 2 , then find the polynomial whose zeroes are 3alpha and 3beta .

If alpha and beta are the two zeroes of the quadratic polynomial x^2-3x+7 , find a quadratic polynomial whose zeroes are 1/alpha and 1/beta .

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

If alpha,beta , are the zeroes of the polynomial ax^2+bx+c ,then alpha^2+beta^2 =

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 .

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

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 .