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The equation formed by decreasing each root of $a x^{2} + b x + c = 0$ by 1 is $2 x^{2} + 8 x + 2 = 0$ , then

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b + c = 0

a = b

a + b = 0

b = c

answer is B.

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Detailed Solution

$a x^{2} + b x + c = 2 {(x - 1)}^{2} + 8 (x - 1) + 2$

$\Rightarrow a = 2 k, b = 4 k, c = - 4 k$

$\Rightarrow b + c = 0$

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