document.write( "Question 554524: Describe the nature and the number of the solutions of 2x^2-7x+9=x+1 \n" ); document.write( "

Algebra.Com's Answer #361368 by josmiceli(19441) $\"\"$ $\"About$

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This is determined by what is called the \" discriminant \"
\n" ); document.write( "This is $\"+b%5E2+-+4a%2Ac+\"$ in the formula for the roots
\n" ); document.write( "which is $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( "In this case:
\n" ); document.write( " $\"+2x%5E2-7x%2B9=x%2B1+\"$
\n" ); document.write( " $\"+2x%5E2+-7x+-+x%2B+9+-+1+=+0+\"$
\n" ); document.write( " $\"+2x%5E2+-+8x+%2B+8+=+0+\"$
\n" ); document.write( " $\"+x%5E2+-+4x+%2B+4+=+0+\"$
\n" ); document.write( " $\"+a+=+1+\"$
\n" ); document.write( " $\"+b+=+-4+\"$
\n" ); document.write( " $\"+c+=+4+\"$
\n" ); document.write( " $\"+b%5E2+-+4a%2Ac+=+%28-4%29%5E2+-+4%2A1%2A4+\"$
\n" ); document.write( " $\"+b%5E2+-+4a%2Ac+=+16+-+16+\"$
\n" ); document.write( "The discriminant is zero, which means there is 1 solution,
\n" ); document.write( "which is called a double root. Here's a plot of the
\n" ); document.write( "equation. Notice it touches the x-axis at 1 point
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+x%5E2+-+4x+%2B+4+%29+\"$ \n" ); document.write( "

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