2024 · Q10
Let p, q be the roots of the equation x²+mx-n=0 and m, n be the roots of the equation x²+px-q=0 (m, n, p, q are non-zero numbers). Which of the following statements is/are correct?
- Im(m+n)=-1
- IIp+q=1 Select the answer using the code given below:
Elementary MathematicsAlgebra
- AI only
- BII only
- CBoth I and II
- DNeither I nor II
Explanation
From the first equation p+q = −m and pq = −n; from the second m+n = −p and mn = −q. Combining the sum and product relations forces p = m = −1 and q = n = 2 (check: (−1)+2 = 1 = −m and (−1)(2) = −2 = −n). Then m(m+n) = (−1)(−1+2) = −1, so I is correct; p+q = −1+2 = 1, so II is correct. Both statements hold — option C.