Given that x=2 is a root of p(x)=x^4-3x^3-18x^2+90x-100, find the other roots (real and nonreal).
+14929 Given that x=2 is a root of p(x)=x^4-3x^3-18x^2+90x-100, find the other roots (real and nonreal).
Hello Guest!
\(x_1=2\)
\((x^4-3x^3-18x^2+90x-100)\) : \((x-2)\)= \(x^3 - x^2 - 20 x + 50\)
\(\underline{x^4-2x^3}\)
\(-x^3-18x^2\)
\(\underline{-x^3\ +\ 2x^2}\)
\(-20x^2+90x\)
\(\underline{-20x^2+40x}\)
\(50x-100\)
\(\underline{50x-100}\)
0
\(x_2=-5\)
\((x^3 -\ x^2 - 20 x + 50)\) : \((x+5)\) = \(x^2-6x+10\)
\(\underline{x^3+5x^2} \)
\(-6x^2-20x\)
\(\underline{-6x^2-30x} \)
\(10x+50\)
\(\underline{ 10x+50} \)
0
\(x^2-6x+10=0\)
\(x=3\pm \sqrt{9-10}\)
\(x_3=3+i\\ x_4=3-i\)
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