1.

0, The equation formed by decreasing each root of the equation ` a x^2 + bx + c = 0` by 1 is ` 2 x^2 + 8x + 2 = 0` then

Answer» Let `alpha,beta ` are the roots of equation `ax^2+bc+c = 0`
Then, `alpha-1` and `beta-1` are the roots of equation `2x^2+8x+2 = 0`
Then, sum of roots, ` (alpha-1)+(beta-1) = -8/2`
`=>alpha+beta = -4+2`
`=>alpha+beta = -2->(1)`
Product of roots, ` (alpha-1)(beta-1) = 2/2`
`=>alphabeta-alpha-beta+1 = 1`
`=>alphabeta -(alpha+beta) = 0`
`=>alphabeta = alpha+beta`
`=>alphabeta = -2->(2)`
As, `alpha` and `beta` are the roots of `ax^2+bx+c = 0`
`:. -b/a = alpha+beta and c/a = alphabeta`
`=> -b/a = -2 and c/a = -2`
`=>b = 2a and ca= -2a`
`=>b=-c`
So, option `2` is the correct option.


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