document.write( "Question 268002: How do you know if a quadratic equation will have one,two, or no solutions? how do you find a quadratic equation if you are only given the solution? Is it possible to have different quadratic equations with the same solution? explain \n" ); document.write( "
Algebra.Com's Answer #196576 by ankor@dixie-net.com(22740)\"\" \"About 
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How do you know if a quadratic equation will have one,two, or no solutions?
\n" ); document.write( "You use the discriminant rules
\n" ); document.write( "In the form ax^2 + bx + c, the discriminant: D = -b^2 - 4*a*c
\n" ); document.write( "If D > 0 we have two real number solutions that are not equal
\n" ); document.write( "If D = 0 we have one real solution (a double root)
\n" ); document.write( "If D < 0 we have two complex (non-real) number solutions
\n" ); document.write( ":
\n" ); document.write( "how do you find a quadratic equation if you are only given the solution?
\n" ); document.write( "An example would be easy to understand. Say we have two solutions (roots)
\n" ); document.write( "x = 7, x = -3
\n" ); document.write( "They can be derived from the factors
\n" ); document.write( "(x-7)(x+3) = 0
\n" ); document.write( "FOIL
\n" ); document.write( "x^2 + 3x - 7x - 21 = 0
\n" ); document.write( "y = x^2 - 4x - 21 would be the equation
\n" ); document.write( ":
\n" ); document.write( "Is it possible to have different quadratic equations with the same solution?
\n" ); document.write( "Yes, the equation y = -x^2 + 4x + 21 will have the same solutions as the one above altho the vertex value of y will be different
\n" ); document.write( ":
\n" ); document.write( "Illustrated by the graph
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-6%2C+10%2C+-30%2C+30%2C+-x%5E2%2B4x%2B21%2C+x%5E2-4x-21%29+\"
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