Let p, q be the roots of the equation x^2+mx-n=0 and m, n be the roots of the equation x^2+px-q=0 (m, n, p, q are non-zero numbers). Which of the following statements is/are correct?<br>I. m(m+n)=-1<br>II. p+q=1

Explanation

From sum/product of roots: p+q = -m \implies p+m = -q and m+n = -p \implies p+m = -n, implying q=n. Since pq = -n \implies pn = -n \implies p=-1. Also mn = -q \implies mn = -n \implies m=-1. Then -1+q = 1 \implies q=2=n. Checking I: m(m+n) = -1(-1+2) = -1 (True). II: p+q = -1+2 = 1 (True).

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