`a((alpha^2)/beta+(beta^2)/alpha)+b(alpha/beta+beta/alpha)`

If alpha and beta are roots of ax^(2) + bx + c = 0 , then find the value of a((alpha^(2) + beta^(2))/(beta alpha)) + b((alpha)/(beta) + (beta)/(alpha))

If alpha and beta are the roots of the equation 3x^(2) - 5x + 2 = 0 , find the value of (i) (alpha)/(beta) + (beta)/(alpha) (ii) alpha-beta (iii) (alpha^(2))/(beta) + (beta^(2))/(alpha)

If alpha and beta are the zeros of the quadratic polynomial f(x)=ax^(2)+bx+c, then evaluate: alpha^(2)+beta^(2)( ii) (alpha)/(beta)+(beta)/(alpha)( iii) alpha^(3)+beta^(3)(1)/(a^(3))+(1)/(beta^(3))(v)(alpha^(2))/(beta)+(beta^(2))/(alpha)

IF alpha , beta are the roots of x^2 - ax +b=0 , then the whose roots are (alpha + beta ) /( alpha ) , (alpha + beta)/( beta) is

If alpha,beta are non-real roots of ax^(2)+bx+c=0,(a,b,c in R), then (A)alpha beta=1(B)alpha=beta(C)(a beta)/(alpha beta)=1(D)alpha=bar(beta)

(alpha + beta)^(2) - 2 alpha beta =

If alpha, beta are the roots of the quadratic equation x^2 + bx - c = 0 , the equation whose roots are b and c , is a. x^(2)+alpha x- beta=0 b. x^(2)-[(alpha +beta)+alpha beta]x-alpha beta( alpha+beta)=0 c. x^(2)+[(alpha + beta)+alpha beta]x+alpha beta(alpha + beta)=0 d. x^(2)+[(alpha +beta)+alpha beta)]x -alpha beta(alpha +beta)=0

If alpha, beta are the roots of the quadratic equation x^2 + bx - c = 0 , the equation whose roots are b and c , is a. x^(2)+alpha x- beta=0 b. x^(2)-[(alpha +beta)+alpha beta]x-alpha beta( alpha+beta)=0 c. x^(2)+[(alpha + beta)+alpha beta]x+alpha beta(alpha + beta)=0 d. x^(2)+[(alpha +beta)+alpha beta)]x -alpha beta(alpha +beta)=0

Prove that | alpha+sqrt(alpha^(2)-beta^(2))|+| alpha-sqrt(alpha^(2)-beta^(2))|=| alpha+beta|+| alpha-beta| where alpha,beta are complex numbers.