document.write( "Question 107107: i am completely lost as to how to even start this problem. Can anyone help me? find the zeros of (2x-7)^2(x^2-9)and state the multiplicity of each. thanks so much!!!! \n" ); document.write( "

Algebra.Com's Answer #77936 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
find the zeros of\r
\n" ); document.write( "\n" ); document.write( " $\"%282x-7%29%5E2%28x%5E2-9%29\"$ \r
\n" ); document.write( "\n" ); document.write( "First, you can write $\"%282x-7%29%5E2\"$ as $\"%282x-7%29%282x-7%29\"$ \r
\n" ); document.write( "\n" ); document.write( "And $\"%28x%5E2-9%29\"$ as $\"+%28x-3%29%28x%2B3%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Then you will have:\r
\n" ); document.write( "\n" ); document.write( " $\"%282x-7%29%282x-7%29+%28x-3%29%28x%2B3%29\"$
\n" ); document.write( "Zeros: product is equal to $\"0\"$ if one factor is equal to $\"0\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"2x-7=0\"$ ЕЕЕ => Е $\"2x+=+7\"$ Е => $\"x+=+7%2F2\"$ ....first and secon zero ( we have $\"2x+-7\"$ two times
\n" ); document.write( "Or
\n" ); document.write( " $\"x-3+=+0\"$ ЕЕЕ =>Е $\"x+=+3\"$ ....third zero
\n" ); document.write( "Or
\n" ); document.write( " $\"x+%2B+3+=+0\"$ ЕЕ..=> Е $\"x+=+-3\"$ ....fourth zero\r
\n" ); document.write( "\n" ); document.write( "check:\r
\n" ); document.write( "\n" ); document.write( " $\"%282x-7%29%5E2%28x%5E2-9%29\"$ \r
\n" ); document.write( "\n" ); document.write( "plug in zeros:\r
\n" ); document.write( "\n" ); document.write( "if $\"x=7%2F2\"$
\n" ); document.write( "

(since one factor is $\"0\"$
\n" ); document.write( "Or
\n" ); document.write( " $\"x=3\"$
\n" ); document.write( " $\"%282%2A3-7%29%5E2%283%5E2-9%29+=+%286-7%29%5E2%289-9%29+=1%2A0+=+0\"$
\n" ); document.write( "Or
\n" ); document.write( " $\"x+=+-3\"$
\n" ); document.write( " $\"%282%2A%28-3%29-7%29%5E2%28%28-3%29%5E2-9%29+=+%28-6-7%29%5E2%289-9%29+=1%2A0+=+0\"$
\n" ); document.write( " \n" ); document.write( "

\n" );