document.write( "Question 41623: Find all the real values of x for which the function: f(x) = 18x^3 - 33x^2 + 20x – 4 becomes zero. \n" ); document.write( "

Algebra.Com's Answer #26898 by psbhowmick(878) $\"\"$ $\"About$

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$\"f%28x%29+=+18x%5E3+-+33x%5E2+%2B+20x\"$ - 4\r
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\n" ); document.write( "\n" ); document.write( "By trial we put x = $\"1%2F2\"$ .
\n" ); document.write( "We find that $\"f%281%2F2%29+=+0\"$ .
\n" ); document.write( "So, by the Remainder theorem, (2x - 1) must be a factor of f(x).\r
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\n" ); document.write( "\n" ); document.write( "Now, let us arrrange f(x) in such way that (2x - 1) can be taken as a factor.
\n" ); document.write( " $\"f%28x%29+=+18x%5E3+-+33x%5E2+%2B+20x+%96+4\"$
\n" ); document.write( "= $\"+9x%5E2%282x-1%29+-+12x%282x-1%29+%2B+4%282x-1%29\"$
\n" ); document.write( "= $\"%282x-1%29%289x%5E2-12x%2B4%29\"$
\n" ); document.write( "= $\"%282x-1%29%28%283x%29%5E2+-+2%2A%283x%29%2A2+%2B+2%5E2%29\"$
\n" ); document.write( "= $\"%282x-1%29%283x-2%29%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Hence the function becomes zero when 2x - 1 = 0 i.e. x = $\"1%2F2\"$ or when 3x - 2 = 0 i.e. x = $\"2%2F3\"$ . \n" ); document.write( "

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