document.write( "Question 745519: Find the number of real -number solutions of each equation\r
\n" ); document.write( "\n" ); document.write( "1. x^2+8=0
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Algebra.Com's Answer #852542 by ikleyn(52969) $\"\"$ $\"About$

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\n" ); document.write( "Find the number of real -number solutions of each equation
\n" ); document.write( "1. x^2+8=0
\n" ); document.write( "2. 3x^2-9x=-5
\n" ); document.write( "3. x^2+4x=-4
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document.write( "(1)  x^2 + 8 = 0.\r\n" );
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document.write( "     This equation has no real solutions, \r\n" );
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document.write( "     because its left side is always positive (strictly greater than zero),\r\n" );
document.write( "     therefore, it can not be equal to zero.\r\n" );
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document.write( "     The number of real solutions is zero.\r\n" );
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document.write( "(2)  3x^3 - 9x = -5.\r\n" );
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document.write( "     Write this quadratic equation in the standard form\r\n" );
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document.write( "         3x^2 - 9x + 5 = 0.\r\n" );
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document.write( "     \r\n" );
document.write( "     Use the discriminant of this equation\r\n" );
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document.write( "         d = b^2 - 4ac = (-9)^2 - 4*3*5 = 81 - 60 = 21.\r\n" );
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document.write( "     The discriminant is positive number - hence, this equation has two real solutions.\r\n" );
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document.write( "(3)  x^2 + 4x = -4.\r\n" );
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document.write( "     Write this quadratic equation in the standard form\r\n" );
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document.write( "         x^2 + 4x + 4 = 0.\r\n" );
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document.write( "     Left side is a perfect square  (x+2)^2.\r\n" );
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document.write( "     So, your equation has the form\r\n" );
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document.write( "         (x+2)^2 = 0.\r\n" );
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document.write( "     It has one root x = -2.\r\n" );
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document.write( "     The number of solutions is 1.\r\n" );
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\n" ); document.write( "\n" ); document.write( "At this point, the problem is solved completely: all questions are answered.
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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