Please solve q 79?

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Answer 1 · 2018-04-19T08:06:32

The answer is #=17.5#

Let the cubic polynomial be

#p(x)=x^3+bx^2+cx+d#

Then,

#p(1)=1+b+c+d=1#, #=>#, #b+c+d=0#

#2p(2)=2*(8+4b+2c+d)=1#, #=>#, #4b+2c+d=-15/2#

#3p(3)=3*(27+9b+3c+d)=1#, #=>#, #9b+3c+d=-80/3#

The sum of the roots of #p(x)# is #s=-b#

Solving for #b# in the #3# equations

#{(b+c+d=0),(4b+2c+d=-15/2),(9b+3c+d=-80/3):}#

#<=>#, #{(3b+c=-15/2),(8b+2c=-80/3):}#

#<=>#, #{(6b+2c=-15),(8b+2c=-80/3):}#

#<=>#, #{(2b=-80/3+15=-35/3):}#

#<=>#, #{(b=-35/6):}#

Therefore,

#s=35/6#

and

#3s=35/2=17.5#