if ax^2+2bx+c=0 and a1x^2+b1x+c1=0 have a common root and a/a1, b/b1 and c/c1 are in AP. show that a1, b1 and c1 are GP

Dear student,

Make use of AP:

Since a/a1,b/b1,c/c1 are in AP

Hence 2b/b1=a/a1+c/c1

Now make use of common root property

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