If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of (r + s)^2?
Choose the most appropriate option.
A) 8	B) 2	C) − 2	D) − 3	E) 4
We know that given ax^2 + bx + c = 0, Sum of the roots = -b/a and product of the roots = c/a.   The roots here are -r and -s.   -r - s = -(-2)/1 = r + s = -2   (-r)*(-s) = -15/1 = rs   So one of r and s is -5 and the other is 3. So (r + s)^2 could be 4.   Answer (4)
<result>E</result>
If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of (r + s)^2?