Problem: If three of the roots of x4+ax2+bx+c=0 are 1,2, and 3, then the value of a+c is:
Answer Choices:
A. 35
B. 24
C. −12
D. −61
E. −63
Solution:
1+2+3+r4=0,r4=−6. Since -a represents the sum of the roots taken two at a time and c represents the product of the roots, we have −a=−2−3+6−6+12+18=25 and c=(1)(2)(3)(−6)=−36 ∴a+c=−25−36=−61
or
Solve the system 1+a+b+c=0 to obtain a=−25,b=60,c=−3616+4a+2b+c=0∴a+c=−6181+9a+3b+c=0