Home
Class 12
MATHS
Let alpha,beta,gamma are the real roots ...

Let `alpha,beta,gamma` are the real roots of the equation `x^3+a x^2+b x+c=0(a ,b ,c in Ra n da!=0)dot` If the system of equations `(inu ,v ,a n d w)` given by `alphau+betav+gammaw=0` `betau+gammav+alphaw=0` `gammau+alphav+betaw=0` has non-trivial solutions then the value of `a^2//b` is ________.

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

Let alpha, beta and gamma are the roots of equation x^(3) + ax^(2) + bx + c = 0 (a, b, c in R, a != 0) . If system of equations alphax + betay + gammaz = 0 betax + gammay + alphaz = 0 gammax + alphay + betaz = 0 has non trivial solution then the value of ((a^2)/(b)) is :

Let alpha ,beta and gamma be the roots of the equations x^(3) +ax^(2)+bx+ c=0,(a ne 0) . If the system of equations alphax + betay+gammaz=0 beta x +gamma y+ alphaz =0 and gamma x =alpha y + betaz =0 has non-trivial solution then

Let a, b, c be non-zero real roots of the equation x^(3)+ax^(2)+bx+c=0 . Then

Let system of equation alphau+betav+gammaw=0 , betau+gammav+alphaw=0 , gammau+alphav+betaw=0 has non trial solution and alpha, beta, gamma are distinct root x^3+ax^2+bx+c=0 then find value of a^2/b

Let alpha , beta be the roots of the equation (x-a) (x-b) = c , cne 0 , then find the roots of the equation (x - alpha) (x -beta) + c = 0

If alpha and beta ( alpha

If alpha and beta are the roots of the equation x^(2)-ax+b=0 and A_(n)=alpha^(n)+beta^(n)

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