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

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(A) Given the quadratic equation $(b - c)x^2 + (c - a)x + (a - b) = 0$. For a quadratic equation $Ax^2 + Bx + C = 0$,if the roots are equal,the discri

Vedclass · Accepted Answer

Arithmetic Progression

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(A) Given the quadratic equation $(b - c)x^2 + (c - a)x + (a - b) = 0$. For a quadratic equation $Ax^2 + Bx + C = 0$,if the roots are equal,the discriminant $D = B^2 - 4AC = 0$. Here,$A = (b - c)$,$B = (c - a)$,and $C = (a - b)$. Substituting these into the discriminant formula: $(c - a)^2 - 4(b - c)(a - b) = 0$. Expanding the terms: $(c^2 - 2ac + a^2) - 4(ab - b^2 - ac + bc) = 0$. $c^2 - 2ac + a^2 - 4ab + 4b^2 + 4ac - 4bc = 0$. $a^2 + 4b^2 + c^2 + 2ac - 4ab - 4bc = 0$. This can be written as: $(a - 2b + c)^2 = 0$. Therefore,$a - 2b + c = 0$,which implies $2b = a + c$. This is the condition for $a, b, c$ to be in Arithmetic Progression.

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

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