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 $(x - a)(x - b) - c = 0$.Expanding this,we get $x^2 - (a + b)x + ab - c = 0$.Comparing this with

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$a, b$

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(C) Given that $\alpha$ and $\beta$ are the roots of $(x - a)(x - b) - c = 0$.Expanding this,we get $x^2 - (a + b)x + ab - c = 0$.Comparing this with the standard quadratic equation $x^2 - (\alpha + \beta)x + \alpha\beta = 0$,we have:$\alpha + \beta = a + b$ and $\alpha\beta = ab - c$.Now,consider the equation $(x - \alpha)(x - \beta) + c = 0$.Expanding this,we get $x^2 - (\alpha + \beta)x + \alpha\beta + c = 0$.Substituting the values of $(\alpha + \beta)$ and $\alpha\beta$ into this equation:$x^2 - (a + b)x + (ab - c) + c = 0$$x^2 - (a + b)x + ab = 0$$(x - a)(x - b) = 0$.Thus,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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