document.write( "Question 465239: What are the roots of the polynomial ?
\n" ); document.write( "3x^4 + 6x^3 -2x^2 +9x -36 = 0 \n" ); document.write( "
Algebra.Com's Answer #318780 by Ryan O(12)\"\" \"About 
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B-2x%2B-3+=+0\") has the following solutons:
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\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-3=16\".
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\n" ); document.write( " Discriminant d=16 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--2%2B-sqrt%28+16+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+3\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-2%29-sqrt%28+16+%29%29%2F2%5C1+=+-1\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B-2x%2B-3\" can be factored:
\n" ); document.write( " \"1x%5E2%2B-2x%2B-3+=+1%28x-3%29%2A%28x--1%29\"
\n" ); document.write( " Again, the answer is: 3, -1.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-3+%29\"
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Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation \"4+x+%2B+2+y+=+8\" describes a sloping line. For any
\n" ); document.write( " equation ax+by+c = 0, slope is \"-a%2Fb+=+-4%2F2\".
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 8/4 = 2.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 8/2 = 4.
  • Slope is -4/2 = -2.
  • Equation in slope-intercept form: y=-2*x+4.
\"graph%28+500%2C+500%2C+2-8%2C+2%2B8%2C+4-8%2C+4%2B8%2C+-2%2Ax%2B4+%29+\"\n" ); document.write( "
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