If the roots of equation `x^3+a x^2+b=0a r ealpha_1,alpha_2` and `alpha_3(a ,b!=0)` , then find the equation whose roots are `(alpha_1alpha_2+alpha_2alpha_3)/(alpha_1alpha_2alpha_3),(alpha_2alpha_3+alpha_3alpha_1)/(alpha_1alpha_2alpha_3),(alpha_1alpha_3+alpha_1alpha_2)/(alpha_1alpha_2alpha_3)`

If the roots of equation x^(3) + ax^(2) + b = 0 are alpha _(1), alpha_(2), and alpha_(3) (a , b ne 0) . Then find the equation whose roots are (alpha_(1)alpha_(2)+alpha_(2)alpha_(3))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(2)alpha_(3)+alpha_(3)alpha_(1))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(1)alpha_(3)+alpha_(1)alpha_(2))/(alpha_(1)alpha_(2)alpha_(3)) .

If alpha_1, ,alpha_2, ,alpha_n are the roots of equation x^n+n a x-b=0, show that (alpha_1-alpha_2)(alpha_1-alpha_3).......(alpha_1-alpha_n)=n(alpha_1^(n-1)+a)

Let alpha,beta are the roots of x^2+b x+1=0. Then find the equation whose roots are - (alpha+1//beta)and-(beta+1//alpha) .

If alpha ne beta" but "alpha^(2)=5 alpha-3" and "beta^(2)= 5 beta-3 then the equation whose roots are (alpha)/(beta)" and "(beta)/(alpha) is

If alpha and beta are the roots of the equation 3x^(2) - 6x + 1 = 0 form the equation whose roots are (i) alpha^(2) beta, beta^(2) alpha (ii) 2 alpha + beta, 2beta + alpha

If alpha,beta,gamma are the roots of the equation x^3-p x+q=0, then find the cubic equation whose roots are alpha/(1+alpha),beta/(1+beta),gamma/(1+gamma) .

If alpha and beta are the roots of 2x^2-5x+3=0 form the equation whose roots are alpha+beta and 1/alpha+1/beta

If alpha and beta are the roots of the equation 3x^(2) - 4x+1=0 form a quadratic equation whose roots are (alpha^2)/(beta) and beta^(2)alpha .

If alpha,beta are the roots of the equation x^2-2x+3=0 obtain the equation whose roots are alpha^3-3alpha^2+5alpha-2 and beta^3-beta^2+beta=5