If `alpha` and `beta` are the roots of a quadratic equation such that `alpha+beta=2, alpha^4+beta^4=272` , then the quadratic equation is

If alpha and beta are the zeros of a quadratic polynomial such that alpha+beta=24 and alpha-beta=8 , find a quadratic polynomial having alpha and beta as its zeros.

If alpha,beta are the roots of the equation ax^2 + bx +c=0 such that beta < alpha < 0 , then the quadratic equation whose roots are |alpha|,|beta| is given by

If alpha and beta are the roots of the quadratic equation x^(2) + px + q = 0 , then form the quadratic equation whose roots are alpha + (1)/(beta), beta + (1)/(alpha)

If alpha and beta are the roots of the quadratic equation ax^(2)+bx+1 , then the value of 2alpha^(2)beta^(2) is

If alpha and beta are the roots of the quadratic equation px^(2)+qx+1 , Then the value of alphabeta+alpha^(2)beta^(2) is

If alpha and beta are the complex cube roots of unity, show that alpha^4+beta^4 + alpha^-1 beta^-1 = 0.

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0. a n dalpha^2,beta are the roots of quadratic equation x^2-q x+8=0, then find p ,q,alpha,betadot

If alpha and beta are the roots of the quadratic equation ax^(2)+bx+1 , then the value of (1)/(alpha beta)+(alpha+beta) is

Let alpha and beta be the roots of the quadratic equation ax^(2)+bx+c=0, c ne 0, then form the quadratic equation whose roots are (1-alpha)/(alpha) and (1-beta)/(beta) .

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0a n dalpha^2,beta is the roots of quadratic equation x^2-q x+8=0 , then the value of rifr/8 is the arithmetic mean of p a n d q , is