document.write( "Question 171214: In the equation ax^2+bx+c=0, the value of b^2-4ac is called the _______ of the quadratic equation. What does this value tell you about the real roots of the equation. \n" ); document.write( "

Algebra.Com's Answer #126430 by solver91311(24713) $\"\"$ $\"About$

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$\"b%5E2-4ac\"$ is called the discriminant of the quadratic equation, $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29+\"$ . Note that this is the expression under the radical in the quadratic equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"DELTA\"$ is the symbol for the discriminant, so $\"DELTA=b%5E2-4ac\"$ \r
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\n" ); document.write( "\n" ); document.write( "If $\"DELTA=0\"$ then there is a single root to the quadratic with multiplicity of 2 and that root is $\"x=%28-b%29%2F2a\"$ . The term multiplicity of 2 arises from the fact that every quadratic can be represented as two factors: $\"%28x-r%29%28x-s%29=0\"$ where $\"r\"$ and $\"s\"$ can be either complex or real numbers. In the case of $\"DELTA=0\"$ , $\"r=s\"$ .\r
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\n" ); document.write( "\n" ); document.write( "If $\"DELTA%3E0\"$ then there are two distinct real number roots.\r
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\n" ); document.write( "\n" ); document.write( "If $\"DELTA%3C0\"$ then there is a conjugate pair of complex roots of the form $\"alpha%2B-beta%2Ai\"$ where $\"i\"$ is the imaginary number defined by $\"i%5E2=-1\"$ \n" ); document.write( "

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