CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

If roots of the equation f(x)=x612x5+bx4+cx3+dx2+ex+64=0 are positive, then the remainder when f(x) is divided by x-1 is 


Your Answer
A
2
Correct Answer
B
1
Your Answer
C
3
Your Answer
D
10

Solution

The correct option is B 1
Let the roots of the equation x612x5+bx4+cx3+dx2+ex+64=0 be xi, i=1, 2, 3, 4, 5, 6.Now, Sum of roots =Coefficient of x5Coefficient of x6x1+x2+x3+x4+x5+x6=12and Product of roots=Constant termCoefficient of x6x1x2x3x4x5x6=64Thus, A.M. (x1, x2, x3, x4, x5, x6)=x1+x2+x3+x4+x5+x66=2G.M.(x1, x2, x3, x4, x5, x6)=(x1x2x3x4x5x6)1/6                                             =(64)1/6=2A.M. = G.M.x1=x2=x3=x4=x5=x6=2Hence, the given equation is equivalent to(x2)6=0or, x612x5+60x4160x3+240x2192x+64=0f(1)=112+60160+240192+64=1
 

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More



footer-image