If `alpha,beta` are the roots of the equations `x^2-2x+3=0` then find the numerical value of P and Q

IF alpha and beta are the roots of the equation x^2+alphax+beta=0 then find the numerical values of alpha and beta . [Here , alphanebeta,alphane0,betane0 ]

Given that alpha and beta are the roots of the equation x^(2)-x+7=0 , find (i) The numerical value of (alpha)/(beta+3)+(beta)/(alpha+3) , (ii) an equation whose roots are (alpha)/(beta+3) and (beta)/(alpha+3) .

If alpha, beta are the roots of the equation 2x^2+5x+3=0 , then find the value of beta/alpha + alpha/beta .

If alpha and beta are the roots of the equation x^(2) -x+7=0 , then find the value of alpha^(2) + beta^(2) .

If alpha and beta is the root of the equation x^2-3x+2=0 then find the value of alpha^2 + beta^2

If alpha and beta are the roots of the equation 2x^2+3x-6 then find the value of alpha^2+beta^2

If alpha,beta are the roots of the equation x^(2)+x+1=0 , find the value of alpha^(3)-beta^(3) .

If alpha and beta are the roots of the equation x^(2) - 2x + 4 = 0 , then what is the value of alpha^(3) + beta^(3) ?

If alpha,beta,gamma are the roots of the equation x^3+p x^2+q x+r=0, then find he value of (alpha-1/(betagamma))(beta-1/(gammaalpha))(gamma-1/(alphabeta)) .

If alpha,beta,gamma are the roots of the equation x^3+p x^2+q x+r=0, then find he value of (alpha-1/(betagamma))(beta-1/(gammaalpha))(gamma-1/(alphabeta)) .