The roots of the quadratic equation (a + b - | vedclass

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(D) For a quadratic equation $Ax^2 + Bx + C = 0$,if $A + B + C = 0$,then $x = 1$ is always a root.Here,$A = a + b - 2c$,$B = -(2a - b - c)$,and $C = a

Vedclass · Accepted Answer

None of these

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(D) For a quadratic equation $Ax^2 + Bx + C = 0$,if $A + B + C = 0$,then $x = 1$ is always a root.Here,$A = a + b - 2c$,$B = -(2a - b - c)$,and $C = a - 2b + c$.Sum of coefficients: $A + B + C = (a + b - 2c) - (2a - b - c) + (a - 2b + c) = a + b - 2c - 2a + b + c + a - 2b + c = (a - 2a + a) + (b + b - 2b) + (-2c + c + c) = 0 + 0 + 0 = 0$.Since the sum of coefficients is $0$,$x_1 = 1$ is a root.The product of roots is $\frac{C}{A} = \frac{a - 2b + c}{a + b - 2c}$.Since $x_1 	imes x_2 = \frac{a - 2b + c}{a + b - 2c}$ and $x_1 = 1$,the second root is $x_2 = \frac{a - 2b + c}{a + b - 2c}$.Comparing this with the given options,none of the options $A, B,$ or $C$ match the calculated roots. Therefore,the correct option is $D$.

The roots of the quadratic equation $(a + b - 2c)x^2 - (2a - b - c)x + (a - 2b + c) = 0$ are

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