document.write( "Question 1209300: Solve the inequality x^3 + 4x > 5x^2 - 20x + 8. Write your answer in interval notation. \n" ); document.write( "

Algebra.Com's Answer #848123 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( " $\"x%5E3+%2B+4x+%3E+5x%5E2+-+20x+%2B+8\"$

\n" ); document.write( "Rewrite the inequality with all non-zero terms on the left:

\n" ); document.write( " $\"x%5E3-5x%5E2%2B24x-8%3E0\"$

\n" ); document.write( "Use a graphing utility to find the equation has a single real root at approximately 0.35814. Since the leading coefficient is positive, the inequality is true for all x greater than that root.

\n" ); document.write( "ANSWER (approximately): (0.35814,infinity)

\n" ); document.write( "If the polynomial had three rational roots, finding the exact solution to the inequality would be good exercise in formal algebra. But since the polynomial has only one real root, which is irrational, finding the approximate answer using a graphing utility is the sensible way to go.

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