If the roots of the equation a(b - c)x^2 + b( | vedclass

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(C) For a quadratic equation $Ax^2 + Bx + C = 0$,the roots are equal if the discriminant $D = B^2 - 4AC = 0$.Here,$A = a(b - c)$,$B = b(c - a)$,and $C

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$H.P.$

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(C) For a quadratic equation $Ax^2 + Bx + C = 0$,the roots are equal if the discriminant $D = B^2 - 4AC = 0$.Here,$A = a(b - c)$,$B = b(c - a)$,and $C = c(a - b)$.Sum of coefficients: $A + B + C = a(b - c) + b(c - a) + c(a - b) = ab - ac + bc - ba + ca - cb = 0$.Since the sum of coefficients is $0$,$x = 1$ is one of the roots.Because the roots are equal,both roots must be $1$.For a quadratic equation $Ax^2 + Bx + C = 0$,the product of roots is $C/A$.Therefore,$1 	imes 1 = \frac{c(a - b)}{a(b - c)}$.$a(b - c) = c(a - b) \Rightarrow ab - ac = ac - bc$.$ab + bc = 2ac$.Dividing both sides by $abc$,we get $\frac{1}{c} + \frac{1}{a} = \frac{2}{b}$.This condition implies that $a, b, c$ are in Harmonic Progression $(H.P.)$.

If the roots of the equation $a(b - c)x^2 + b(c - a)x + c(a - b) = 0$ are equal,then $a, b, c$ are in

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