Show that the solutions of the equation `[(x,y),(z,t)]^2=0 are[(x,y),(z,t)]=[(+-sqrt(alphabeta),-beta),(alpha,+-sqrt(alphabeta))]`, where `alpha,beta` are arbitrary.

If alpha,beta are the roots of the equation ax^(2)-bx+b=0 , prove that sqrt((alpha)/(beta))+sqrt((beta)/(alpha))-sqrt((b)/(a))=0 .

If alpha,beta are the roots of the equation 3x^(2)-6x+4=0 , find the value of ((alpha)/(beta)+(beta)/(alpha))+2((1)/(alpha)+(1)/(beta))+3alphabeta .

int _(alpha)^(beta) sqrt((x-alpha)/(beta -x)) dx is equal to

If alpha and beta are roots of the equation x^(2)-2x+1=0 , then the value of (alpha)/(beta)+(beta)/(alpha) is

If the roots of the equation a x^2-b x+c=0a r ealpha,beta, then the roots of the equation b^2c x^2-a b^(2x)+a^3=0 are 1/(alpha^3+alphabeta),1/(beta^3+alphabeta) b. 1/(alpha^2+alphabeta),1/(beta^2+alphabeta) c. 1/(alpha^4+alphabeta),1/(beta^4+alphabeta) d. none of these

If alpha and beta ( alpha'<'beta') are the roots of the equation x^2+b x+c=0, where c<0

If alpha, beta are the roots of the equation x^(2)+alphax + beta = 0 such that alpha ne beta and ||x-beta|-alpha|| lt alpha , then

If alpha,beta are the roots of the equation x^(2)+px+q=0 , find the value of (a) alpha^(3)beta+alphabeta^(3) (b) alpha^(4)+alpha^(2)beta^(2)+beta^(4) .

If alpha and beta are the roots of the equation x^2+sqrt(alpha)x+beta=0 then the values of alpha and beta are -

If alpha and beta are the zeros of the quadratic polynomial p(s)=3s^2-6s+4 , find the value of alpha/beta+beta/alpha+2(1/alpha+1/beta)+3alphabeta .