If (x+k) is the HCF of x^2+p x+q and {x}^2+˙{ {q} x}+ {p}, where {p} \neq {q}, then what is the value of {k} ?

UPSC CDS 2 2022 Math Paper

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If (x+k) is the HCF of x2+px+q and x2+˙qx+p, where p≠q, then what is the value of k ?

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