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Algebra of Limits

If α, β are t...

Question

If $α, β$ are the roots of $a x^{2} + b x + c = 0$ , the correct statements about the equation a ${(x - 2)}^{2}$ + b(x - 2) + c = 0 is

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Solution

The correct option is B

$α, β$ are the roots of a $x^{2}$ + bx + c = 0

$\Rightarrow a α^{2} + b α + c = 0 a n d a β^{2} + b β + c = 0$ clearly, if we substitute $α$ + 2

and $β$ + 2 in a ${(x - 2)}^{2}$ + b(x - 2) + c, we get

$a (α + 2 - 2)^{2} + b (α + 2 - 2) + c = a α^{2} + b α + c$

= 0

$\Rightarrow α + 2 a n d β + 2$ are the roots.

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