document.write( "Question 1181964: How many real number solutions does the equation y=2x^2−8x+8 have? \n" ); document.write( "
Algebra.Com's Answer #811921 by greenestamps(13198)\"\" \"About 
You can put this solution on YOUR website!


\n" ); document.write( "The question you ask is undoubtedly NOT the question you intended to ask.

\n" ); document.write( "The equation y=2x^2-8x+8 has an infinite number of real number solutions. Pick any number you want for x and plug into the equation to find y.

\n" ); document.write( "(x,y) = (0,8) is a solution
\n" ); document.write( "(x,y) = (1,2) is a solution
\n" ); document.write( "(x,y) = (sqrt(3),14-8*sqrt(3)) is a solution

\n" ); document.write( "and so on, ad infinitum....

\n" ); document.write( "The question you INTENDED to ask was either \"how many distinct roots does the equation y=2x^2-8x+8 have?\" or \"how many solutions does the equation 2x^2-8x+8=0 have?\"

\n" ); document.write( "The answer to that question is \"one\".

\n" ); document.write( "2x^2-8x+8=0
\n" ); document.write( "x^2-4x+4=0
\n" ); document.write( "(x-2)(x-2)=0

\n" ); document.write( "The equation has one real number solution: x=2.

\n" ); document.write( "The equation is quadratic, so it has two roots; but the two roots are the same, so it has one distinct root.

\n" ); document.write( "In summary, using correct mathematical language....

\n" ); document.write( "The equation y=2x^2-8x+8 has one distinct real root

\n" ); document.write( "The equation 2x^2-8x+8=0 has one real solution

\n" ); document.write( "The equation y=2x^2-8x+8 has an infinite number of real solutions
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