document.write( "Question 239121: What is the greatest zero of the function $\"f%28g%29=x%5E2-25x%2B66\"$ \n" ); document.write( "

Algebra.Com's Answer #175629 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
(I assume you mean) $\"f%28x%29=x%5E2-25x%2B66\"$
\n" ); document.write( "The roots (or zeros) of a function are the x values that make the function value a zero. So we are solving
\n" ); document.write( " $\"0=x%5E2-25x%2B66\"$

\n" ); document.write( "To find the roots (or zeros) of a quadratic function like this one, you can use the quadratic formula or, if it's possible, use factoring. This quadratic factors pretty easily so that's what I'll use.
\n" ); document.write( "Factor the right side:
\n" ); document.write( " $\"0+=+%28x-22%29%28x-3%29\"$
\n" ); document.write( "The Zero Product Property tells us that this or any product can be zero only if one or more of the factors is zero. This tells us that:
\n" ); document.write( " $\"x-22+=+0\"$ or $\"x+-+3+=+0\"$
\n" ); document.write( "Solving each of these we get:
\n" ); document.write( " $\"x+=+22\"$ or $\"x+=+3\"$
\n" ); document.write( "The largest root (or zero) of the equation, therefore, is 22.

\n" ); document.write( "(Note: If you choose to use the quadratic formula, you will get the same answers (if you use it correctly).) \n" ); document.write( "

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