Q20 of 47 Page 1

If the roots of the equation (c2 – ab)x2 – 2(a2 – bc)x + b2 – ac = 0 in x are equal, then show either a = 0 or a3 + b3 + c3 = 3abc.

Given has equal roots


We know that, for if it has equal roots


So, applying this to our given equation, we get








So,


Conclusion: Therefore, if roots of


are equal then then a=0 or



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