Let alpha be a repeated root of a quad...

Let `alpha` be a repeated root of a quadratic equation `f(x)=0 ` and `A(x),B(x),C(x)` be polynomials of degrees 3, 4, and 5, respectively, then show that `|(A(x),B(x),C(x)) ,(A(alpha),B(alpha),C(alpha)),(A '(alpha),B '(alpha),C '(alpha))|` is divisible by `f(x)` , where prime `(')` denotes the derivatives.

Similar Questions

Explore conceptually related problems

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

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

If alpha " and " beta are the roots of the quadratic equation x^2 -5x +6 =0 then find alpha/beta + beta/alpha

If alpha is repeated roots of ax^(alpha)+bx+c=0 then lim_(x rarr a)(tan(ax^(2)+bx+c))/((x-alpha)^(2)) is

If alpha,beta are roots of the equation 2x^(2)+6x+b=0(b<0), then (alpha)/(beta)+(beta)/(alpha) is less than

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 be the roots of the equation (x-a)(x-b)=c and c!=0 ,then roots of the equation (x-alpha)(x-beta)+c=0 are