document.write( "Question 917247: Prove that x=2 is a real zero of y=-x^3+7x^2-55x+90 \n" ); document.write( "

Algebra.Com's Answer #556582 by MathLover1(20849) $\"\"$ $\"About$

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$\"y=-x%5E3%2B7x%5E2-55x%2B90+\"$ factor it first, factor out $\"-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-1%28x%5E3-7x%5E2%2B55x-90%29+\"$ ............write $\"-7x%5E2\"$ as $\"-2x%5E2-5x%5E2\"$ and $\"55x\"$ as $\"45x%2B10x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-%28+x%5E3-5x%5E2%2B45x-2x%5E2%2B10x-90%29\"$ ...group\r
\n" ); document.write( "\n" ); document.write( " $\"y=-%28%28+x%5E3-5x%5E2%2B45x%29-%282x%5E2-10x%2B90%29%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-%28x%28+x%5E2-5x%2B45%29-2%28x%5E2-5x%2B45%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-%28%28x-2%29%28x%5E2-5x%2B45%29%29\"$ ...as you can see one of the factors is $\"x-2\"$ and if we set it equal to zero we get: \r
\n" ); document.write( "\n" ); document.write( " $\"x-2=0\"$ => $\"x=2\"$ which proves that $\"x=2\"$ is a real zero of $\"y=-x%5E3%2B7x%5E2-55x%2B90\"$ \r
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