Find-an-integer-x-that-satisfies-the-equation-x-5-101x-3-999x-2-100900-0-

Question Number 8707 by Sopheak last updated on 22/Oct/16

F i n d a n i n t e g e r x t h a t s a t i s f i e s t h e e q u a t i o n

x^{5} - 101 x^{3} - 999 x^{2} + 100900 = 0

Answered by Rasheed Soomro last updated on 23/Oct/16

The solution is factor of 100900 .

So on trying x = 10 is one solution .

That also means that x - 10 is a factor

of x^{5} - 101 x^{3} - 999 x^{2} + 100900

By synthetic division we can determine

other factor :

| \begin{matrix} 10) & 1 & 0 & - 101 & - 999 & 0 & + 100900 \\ 10 & + 100 & - 10 & - 10090 & - 100900 \\ 1 & 10 & - 1 & - 1009 & - 10090 & [0 \end{matrix} |

So the other factor is

x^{4} + {10 x}^{3} - x^{2} - 1009 x - 10090

The rest roots of the given equation are the

roots of x^{4} + {10 x}^{3} - x^{2} - 1009 x - 10090 = 0

Trying all the possible integer factors of 10090

we learn that there is no other integer solution .

So x = 10