document.write( "Question 177858: Evaluate the discriminant of each equation. How many real and imaginary
\n" ); document.write( "solutions does each have?\r
\n" ); document.write( "\n" ); document.write( "37. x2 + 5x + 6 = 0
\n" ); document.write( "38. 3x2 - 4x + 3 = 0
\n" ); document.write( "39. -2x2 - 5x + 4 = 0
\n" ); document.write( "40. 16x2 - 8x + 1 = 0 \n" ); document.write( "

Algebra.Com's Answer #132862 by solver91311(24713) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "The discriminant is that part of the quadratic equation under the radical, so

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0\"> then the quadratic equation has two real and unequal roots.\r
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then the quadratic equation has two real and equal roots. It is also said that the quadratic has one real root with a multiplicity of 2. This is because the

situation only occurs when the quadratic is a perfect square as in

. Each one of the factors translates to a root of the equation, so there are, in fact, two of them; they just happen to be equal.\r
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then the quadratic equation has a conjugate pair of complex roots of the form

where i is the imaginary number defined by

. Note that unless the real part of the complex number (the a in

) is zero, the roots are not purely imaginary.\r
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\n" ); document.write( "\n" ); document.write( "So, for each of your problems, calculate

and evaluate the character of the roots per the definitions above.\r
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