Problem: If a,b,c, and d are non-zero numbers such that c and d are solutions of x2+ax+b=0 and a and b are solutions of x2+cx+d=0, then a+b+c+d equals
Answer Choices:
A. 0
B. −2
C. 2
D. 4
E. (−1+5​)/2
Solution:
Since the constant term of a quadratic equation is the product of its roots,
b=cd.d=ab
Since the coefficient of the x term of a quadratic equation whose x2 coef. ficient is one is the negative of the sum of its roots. a=c+d,c=a+b, a+c+d=0=a+b+c, and b=d. But the equations b=cd and d=ab imply, since b=dî€ =0. that 1=a=c Therefore, b=d=−2, and a+b+c+d=−2.