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Question
The roots of the equation x2 − 3x − m (m + 3) = 0, where m is a constant, are
Options
A. m, m + 3
B. − m, m + 3
C. m, − (m + 3)
D. −m, − (m + 3)
Solution
The given quadratic equation is x2 − 3x − m (m + 3) = 0.
`rArr x^2-[(m+3)-m]x-m(m+3)=0`
`rArr x^2-(m+3)x+mx-m(m+3)=0`
`rArr x{x-(m+3)}+m{x-(m+3)}=0`
`rArr(x+m){x-(m+3)}=0`
`rArrx+m=0` Or `x-(m+3)=0`
`rArr x=-m` or `x=m+3`
Thus, the roots of the given quadratic equation are −m and m + 3.
The correct answer is B.
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