document.write( "Question 435483: What is the type and how many solutions are there to the following quadratic equation?
\n" ); document.write( "x^2-3x+3=0
\n" ); document.write( "A. one rational solution
\n" ); document.write( "B. two complex solutions
\n" ); document.write( "C. two rational solutions
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Algebra.Com's Answer #301377 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "For any quadratic polynomial equation of the form:\r
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\n" ); document.write( "\n" ); document.write( "Find the Discriminant,

and evaluate the nature of the roots as follows:\r
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\n" ); document.write( "\n" ); document.write( "No calculation quick look: If the signs on

and

are opposite, then

0\"> guaranteed.\r
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0 \ \ \Rightarrow\ \\"> Two real and unequal roots. If

is a perfect square, the quadratic factors over

(the rationals).\r
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One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors. Presuming rational coefficients, the root will be rational as well.\r
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A conjugate pair of complex roots of the form

where

is the imaginary number defined by

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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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$\"The$

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