document.write( "Question 1209689: Find all roots of the polynomial f(x) = 2x^3 - 5x^2 - 2x + 2 - 8x^3 + 11x^2 - 17x + 8. \n" ); document.write( "
Algebra.Com's Answer #849820 by CPhill(1959)\"\" \"About 
You can put this solution on YOUR website!
1. **Combine like terms:**
\n" ); document.write( " f(x) = (2x^3 - 8x^3) + (-5x^2 + 11x^2) + (-2x - 17x) + (2 + 8)
\n" ); document.write( " f(x) = -6x^3 + 6x^2 - 19x + 10\r
\n" ); document.write( "\n" ); document.write( "2. **Rational Root Theorem:** Possible rational roots are of the form p/q, where p is a factor of 10 and q is a factor of -6.\r
\n" ); document.write( "\n" ); document.write( " Possible values for p: ±1, ±2, ±5, ±10
\n" ); document.write( " Possible values for q: ±1, ±2, ±3, ±6\r
\n" ); document.write( "\n" ); document.write( " Possible rational roots: ±1, ±2, ±5, ±10, ±1/2, ±5/2, ±1/3, ±2/3, ±5/3, ±10/3, ±1/6, ±5/6\r
\n" ); document.write( "\n" ); document.write( "3. **Test potential roots:** This is tedious. Let's use a graphing calculator or online polynomial solver.\r
\n" ); document.write( "\n" ); document.write( "Using a calculator, we find the roots are approximately:\r
\n" ); document.write( "\n" ); document.write( "* x ≈ 0.215 + 1.696i
\n" ); document.write( "* x ≈ 0.215 - 1.696i
\n" ); document.write( "* x ≈ 0.570\r
\n" ); document.write( "\n" ); document.write( "There is one real root and two complex roots. It is very difficult to find these roots by hand. Numerical methods are the most practical approach.
\n" ); document.write( " \n" ); document.write( "
\n" );