If alpha, beta are the roots of (x - a)(x - b | vedclass

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(C) Given that $\alpha$ and $\beta$ are the roots of the equation $(x - a)(x - b) = c$.Expanding this,we get $x^2 - (a + b)x + ab = c$,or $x^2 - (a +

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$a, b$

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(C) Given that $\alpha$ and $\beta$ are the roots of the equation $(x - a)(x - b) = c$.Expanding this,we get $x^2 - (a + b)x + ab = c$,or $x^2 - (a + b)x + (ab - c) = 0$.From the properties of quadratic equations,the sum of the roots is $\alpha + \beta = a + b$ and the product of the roots is $\alpha \beta = ab - c$.We need to find the roots of the equation $(x - \alpha)(x - \beta) + c = 0$.Expanding this,we get $x^2 - (\alpha + \beta)x + \alpha \beta + c = 0$.Substituting the values $\alpha + \beta = a + b$ and $\alpha \beta = ab - c$ into the equation,we get:$x^2 - (a + b)x + (ab - c) + c = 0$$x^2 - (a + b)x + ab = 0$This is equivalent to $(x - a)(x - b) = 0$.Therefore,the roots of the equation are $a$ and $b$.

If $\alpha, \beta$ are the roots of $(x - a)(x - b) = c,$ where $c \neq 0,$ then the roots of $(x - \alpha)(x - \beta) + c = 0$ are

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