given that `alpha and beta` are the roots of the equation `x^2=7x+4`. 1) Show that `alpha^3=53alpha+4` 2)find `alpha/beta+ beta/alpha`

Given that alpha and beta are the roots of the equation x^(2)=7x+4 , (i) show that alpha^(3)=53alpha+28 (ii) find the value of (alpha)/(beta)+(beta)/(alpha) .

If alpha and beta are the roots of the equation 3x^(2)+7x+3=0 Find the value of alpha beta:

If alpha and beta be the roots of the equation x^2-1=0 , then show that. alpha+beta=(1)/(alpha)+(1)/(beta)

If alpha and beta are the roots of equation x^2-4x+1=0 , find alpha^3+beta^3

If alpha and beta are the roots of equation x^2-4x+1=0 , find alpha^2+beta^2

IF alpha and beta are the roots of the equation x(x-3)=4, find the value of alpha^2+beta^2 .

Given that alpha and beta are the roots of the equation x^(2)=x+7 Prove that (a)(1)/(alpha)=(alpha-1)/(7)(b)alpha^(3)=8 alpha+7 Find the numerical value of (alpha)/(beta)+(beta)/(alpha)

If alpha and beta are the roots of the equation 4x^(2)+3x+7=0, then (1)/(alpha)+(1)/(beta)=

If alpha and beta are the roots of the quadratic equation x^2-3x-2=0 , then alpha/beta+beta/alpha=