If alpha,beta are the roots of a x^2+b x...

If `alpha,beta` are the roots of `a x^2+b x+c=0,(a!=0)` and `alpha+delta,beta+delta` are the roots of `A x^2+B x+C=0,(A!=0)` for some constant `delta` then prove that `(b^2-4a c)/(a^2)=(B^2-4A C)/(A^2)`

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If the roots of the equation ax^2+bx+c=0 are alpha , beta and the roots of the equation Ax^2+Bx+C=0 are (alpha+delta) and (beta+delta) then show that (b^2-4ac)/a^2=(B^2-4AC)/A^2

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Let alpha and beta be the roots of the equation ax^2+2bx+c =0 and alpha+gamma and beta+gamma be the roots of Ax^2+2Bx+C =0. Then prove that A^2(b^2-ac)=a^2(B^2-AC) .

If alpha,beta are the nonzero roots of a x^2+b x+c=0 and alpha^2,beta^2 are the roots of a^2x^2+b^2x+c^2=0 , then a ,b ,c are in (A) G.P. (B) H.P. (C) A.P. (D) none of these

If alpha,beta are the roots of the equation a x^2+b x+c=0, then find the roots of the equation a x^2-b x(x-1)+c(x-1)^2=0 in term of alpha and betadot

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