document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208922>Question 1208922</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 6k^2 + k = 2 and k > 0, find the value of k.  </SPAN>\n" );
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document.write( "6k^2+k = 2<BR>\n" );
document.write( "6k^2+k-2 = 0\r<BR>\n" );
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document.write( "You can factor or use the quadratic formula as the other tutors have shown.\r<BR>\n" );
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document.write( "Another approach is to use the Rational Root Theorem.<BR>\n" );
document.write( "This is where we divide factors of q over factors of p<BR>\n" );
document.write( "p = 6 = leading coefficient<BR>\n" );
document.write( "q = -2 = last term of the polynomial\r<BR>\n" );
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document.write( "Factors of 6 are: 1,2,3,6<BR>\n" );
document.write( "Factors of 2 are: 1,2\r<BR>\n" );
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document.write( "Dividing those terms gives these possible rational roots<BR>\n" );
document.write( "1, 1/2, 1/3, 1/6, 2, 2/3<BR>\n" );
document.write( "-1, -1/2, -1/3, -1/6, -2, -2/3<BR>\n" );
document.write( "We consider the plus minus of each.\r<BR>\n" );
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document.write( "Then plug each item into 6k^2+k-2 to see if we get zero or not.<BR>\n" );
document.write( "Try k = 1 to get 6k^2+k-2 = 6*(1)^2+1-2 = 5<BR>\n" );
document.write( "The nonzero result means that k = 1 is not a root.\r<BR>\n" );
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document.write( "Now let's try k = 1/2.<BR>\n" );
document.write( "6k^2+k-2 = 6*(1/2)^2+(1/2)-2 = 0<BR>\n" );
document.write( "We get 0 as the result, so it proves k = 1/2 is a root.<BR>\n" );
document.write( "The other root is k = -2/3<BR>\n" );
document.write( "All of the other values will lead to nonzero results, so we can eliminate them. Also keep in mind that any quadratic will have 2 roots.\r<BR>\n" );
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document.write( "We have shown the two roots are k = 1/2 and k = -2/3<BR>\n" );
document.write( "Ignore k = -2/3 since k > 0 was mentioned in the instructions.\r<BR>\n" );
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document.write( "Answer: <font color=red>k = 1/2</font><BR>\n" );
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