If the roots of the equation $x^{2} + a x + b = 0$ are $c$ and $d$ then one of the roots of the equation $x^{2} + (2 c + a) x + c^{2} + a c + b = 0$ is

2 c

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d - c

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c

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2 d

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Solution

The correct option is B $d - c$
Let $f (x) = x^{2} + a x + b$
then $x^{2} + (2 c + a) x + c^{2} + a c + b = f (x + c)$
Thus roots of $f (x + c) = 0$ will be $0, d - c$ .

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