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(B) Let $\alpha$ and $\beta$ be the roots of the equation $ax^2 + bx + c = 0$.From the properties of roots,we have $\alpha + \beta = -b/a$ and $\alpha

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$b = -c$

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(B) Let $\alpha$ and $\beta$ be the roots of the equation $ax^2 + bx + c = 0$.From the properties of roots,we have $\alpha + \beta = -b/a$ and $\alpha\beta = c/a$.The roots of the new equation are $(\alpha - 1)$ and $(\beta - 1)$.The new equation is $2x^2 + 8x + 2 = 0$,which can be written as $x^2 + 4x + 1 = 0$.For the new equation,the sum of roots is $(\alpha - 1) + (\beta - 1) = -4/1 = -4$.Thus,$(\alpha + \beta) - 2 = -4$,which implies $\alpha + \beta = -2$.Substituting $\alpha + \beta = -b/a$,we get $-b/a = -2$,so $b = 2a$.The product of the new roots is $(\alpha - 1)(\beta - 1) = 1/1 = 1$.Expanding this,we get $\alpha\beta - (\alpha + \beta) + 1 = 1$,which simplifies to $\alpha\beta - (\alpha + \beta) = 0$.Substituting $\alpha\beta = c/a$ and $\alpha + \beta = -2$,we get $c/a - (-2) = 0$,so $c/a + 2 = 0$,which means $c = -2a$.Since $b = 2a$ and $c = -2a$,we have $b = -c$.

The equation formed by decreasing each root of $ax^2 + bx + c = 0$ by $1$ is $2x^2 + 8x + 2 = 0$. Then:

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