document.write( "Question 122287: 2. The following equation has degree 4 because the highest power of the variable x is 4:
\n" ); document.write( "x^4 – 3 x^2 + 2 = 0.
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Algebra.Com's Answer #89780 by solver91311(24713)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let \"t=x%5E2\", which means that \"t%5E2=x%5E4\"\r
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document.write( "Now substitute:\r
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document.write( "\"t%5E2-3t%2B2=0\" is factorable\r
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document.write( "\"%28t-1%29%28t-2%29=0\" => \"t=1\" or \"t=2\", so you really don't need the
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document.write( "quadratic formula to solve it.  But since the question asked for it, here
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document.write( "it is\r
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document.write( "a = 1
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document.write( "b = -3
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document.write( "c = 2\r
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document.write( "\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\" 
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document.write( "\"t+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%2A%281%29%2A%282%29+%29%29%2F%282%2A%281%29%29+\" 
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document.write( "\"t+=+%283+%2B-+sqrt%28+9-8+%29%29%2F2\" => \"t=%283%2B1%29%2F2=4%2F2=2\" or \"t=%283-1%29%2F2=2%2F2=1\"\r
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document.write( "And no surprise, the roots are still 1 and 2.\r
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document.write( "But remember \"t=x%5E2\"\r
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document.write( "If \"t=1\" then \"x=%2Bsqrt%281%29\" or \"x=-sqrt%281%29\" => \"x=1\" or \"x=-1\"\r
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document.write( "If \"t=2\" then \"x=%2Bsqrt%282%29\" or \"x=-sqrt%282%29\"\r
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document.write( "This gives us a total of four roots for the original quartic (degree 4)
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document.write( "equation as the Fundamental Theorem of Algebra would lead us to suspect.\r
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document.write( "Just for fun, let's check the notion graphically:\r
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document.write( "\"graph%28600%2C600%2C-5%2C5%2C-5%2C5%2Cx%5E4-3x%5E2%2B2%29\"\r
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document.write( "Note that the graph intersects the x-axis in 4 places and the x-coordinates of
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document.write( "these 4 places are equal to the roots or zeros of the given equation.\r
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document.write( "How very tidy. \n" );
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