Question

Let $a,b,c$ be the three roots of the equation $x^3+x^2-333x-1002=0$ then the value of $a^3+b^3+c^3$.

• A. 2006
• B. 2005
• C. 2003
• D. 2002

Answer 1

Answer: (A)

Let $t$ be the root of the given cubic where $t$ can take values $a,b,c$ hence $t^3+t^2-333t-1002=0$ or $t^3=1002+333t-t^2$ $\therefore \sum t^3=\sum 1002+333\sum t-\sum t^2=3006+333\sum t-\left[{\left(\sum t\right)}^2-2\sum t_1{t}_2\right]$ $\text{ but }\sum t=-1;\sum t_1{t}_2=-333$ ${\therefore }^3+b^3+c^3=3006-333-[1+666]=3006-333-667=3006-1000=2006$