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Lets $n=pq$ with $p$ and $q$ primes

If we know the result of $p+q$, can we factorize $n$ in polynomial time ?

Best regards.

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    polynomial time with respect to what? – 2017-01-02
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    Your thoughts please... (since this is not a 'do my homework for free' service). – 2017-01-02
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    Hope it was homework, but school is far far away..., I mean does knowing the sum of the two factors can help to factorize a number – 2017-01-02

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Suppose $n=pq$ and $p+q=k$, then $p$ and $q$ are the roots of the polynomial $x^2-(p+q)x+pq$ and so they are equal to $\frac{p+q\pm \sqrt{p+q)^2-4pq}}{2}$

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    right, thanks.${}{}{}{}{}$ – 2017-01-02
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    Great observation, but for completeness' sake, maybe including a conclusion about the polynomial time would be nice? – 2017-01-02
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    @SteamyRoot: the time will be polylog, at most $\log^2n$. – 2017-01-02
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    it is $\mathcal O(\log(n))$ as we need to find the square root of a number of size approximately $4n^2$. – 2017-01-02
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    @JorgeFernándezHidalgo: don't you mean like $O(\log n\log\log n\log\log\log n)$ ? – 2017-01-02
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    @YvesDaoust why is there an $n$ all by itself? – 2017-01-02
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    @JorgeFernándezHidalgo: I fixed the typo. – 2017-01-02
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    @YvesDaoust I guess that makes sense ;) – 2017-01-02