document.write( "Question 1209700: Find all roots of the polynomial
\n" ); document.write( "f(x) = x^4 - 5x^3 + 5x^2 + 17x - 42 + 4x^4 + 10x^3 - 18x^2 + 2x - 5. \n" ); document.write( "
Algebra.Com's Answer #849837 by CPhill(1959)\"\" \"About 
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To find the roots of the polynomial f(x) = x^4 - 5x^3 + 5x^2 + 17x - 42 + 4x^4 + 10x^3 - 18x^2 + 2x - 5, we first need to combine the like terms to simplify the polynomial.\r
\n" ); document.write( "\n" ); document.write( "Combining the x^4 terms: x^4 + 4x^4 = 5x^4
\n" ); document.write( "Combining the x^3 terms: -5x^3 + 10x^3 = 5x^3
\n" ); document.write( "Combining the x^2 terms: 5x^2 - 18x^2 = -13x^2
\n" ); document.write( "Combining the x terms: 17x + 2x = 19x
\n" ); document.write( "Combining the constant terms: -42 - 5 = -47\r
\n" ); document.write( "\n" ); document.write( "So, the simplified polynomial is:
\n" ); document.write( "f(x) = 5x^4 + 5x^3 - 13x^2 + 19x - 47\r
\n" ); document.write( "\n" ); document.write( "To find the roots of this quartic polynomial, we can use numerical methods or a computer algebra system. The roots are approximately:\r
\n" ); document.write( "\n" ); document.write( "x ≈ -2.81952163
\n" ); document.write( "x ≈ 1.56441331
\n" ); document.write( "x ≈ 0.12755416 + 1.45424058i
\n" ); document.write( "x ≈ 0.12755416 - 1.45424058i\r
\n" ); document.write( "\n" ); document.write( "These are the four roots of the polynomial. Two are real, and two are complex conjugates.
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