If a, b, c are distinct and the roots of (b-c | vedclass

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(A) Given that the roots of the quadratic equation $(b-c)x^2 + (c-a)x + (a-b) = 0$ are equal,the discriminant $D$ must be $0$. $D = (c-a)^2 - 4(b-c)(a

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arithmetic progression

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(A) Given that the roots of the quadratic equation $(b-c)x^2 + (c-a)x + (a-b) = 0$ are equal,the discriminant $D$ must be $0$. $D = (c-a)^2 - 4(b-c)(a-b) = 0$ Expanding the terms: $(c^2 + a^2 - 2ac) - 4(ab - b^2 - ac + bc) = 0$ $c^2 + a^2 - 2ac - 4ab + 4b^2 + 4ac - 4bc = 0$ $c^2 + a^2 + 2ac + 4b^2 - 4ab - 4bc = 0$ $(c+a)^2 - 4b(a+c) + (2b)^2 = 0$ This is in the form $X^2 - 2XY + Y^2 = 0$,where $X = (c+a)$ and $Y = 2b$. $(c+a - 2b)^2 = 0$ $c+a - 2b = 0$ $2b = a+c$ Since $2b = a+c$,the terms $a, b, c$ are in arithmetic progression $(AP)$.

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

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