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`

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-px+q=0 ,form the quadratic equation whose roots are 2alpha-beta , 2beta-alpha

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

Find the quadratic equation whose roots are given below. -3, 4/3

Find the quadratic equation whose roots are given as sqrt2 +1 and sqrt2 -1 .

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

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 .

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

If 1 is a root of the quadratic equation px^2+x+1/4=0 ,find the value of p.