document.write( "Question 206101: I really need some help for this problems because I have been confuse of this problems since the start and now the Examination is coming near and this is going to be added, I really will appreciate some help in this questions:\r
\n" ); document.write( "\n" ); document.write( "---find the value of k so that the equation $\"+3x%5E2-7x%2Bk=0+\"$ will have equal roots.\r
\n" ); document.write( "\n" ); document.write( "---find the value of k so that the equation $\"+3x%5E2-%285%2Bk%29x-17=0+\"$ will have one roots numerically equal but opposite in sign\r
\n" ); document.write( "\n" ); document.write( "--what should be the range of the value of k so that the equation $\"+2x%5E2%2B3kx-9=0+\"$ will have real and unequal roots.\r
\n" ); document.write( "\n" ); document.write( "---what should be the value of k so that the equation $\"+x%5E2%2B%28k-2%29x%2B4=0+\"$
\n" ); document.write( "will have equal roots? \n" ); document.write( "

Algebra.Com's Answer #155680 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
I really need some help for this problems because I have been confuse of this problems since the start and now the Examination is coming near and this is going to be added, I really will appreciate some help in this questions:\r
\n" ); document.write( "\n" ); document.write( "---find the value of k so that the equation $\"+3x%5E2-7x%2Bk=0+\"$ will have equal roots.
\n" ); document.write( "

\r\n" );
document.write( "Find the discriminant \r\n" );
document.write( "\r\n" );
document.write( "To have equal roots the discriminant must equal 0, so\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To check, we substitute  for  in\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Multiply through by 12 to clear of fractions:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "; \r\n" );
document.write( "  ; \r\n" );
document.write( " ; \r\n" );
document.write( "\r\n" );
document.write( "So the roots are equal. \r\n" );
document.write( "\r\n" );
document.write( "----------------------------------- \r\n" );
document.write( "\r\n" );
document.write( "

\n" ); document.write( "---find the value of k so that the equation $\"+3x%5E2-%285%2Bk%29x-17=0+\"$ will have one roots numerically equal but opposite in sign
\n" ); document.write( "

\r\n" );
document.write( "Then it will have to be true that we also get zero when we \r\n" );
document.write( "substitute  for :\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "And since we started with \r\n" );
document.write( "We can set the left sides equal:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Divide thru by 2\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Factor out x\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( ";  \r\n" );
document.write( "           \r\n" );
document.write( "\r\n" );
document.write( "So the value of k that will cause the\r\n" );
document.write( "roots to be numerically equal but opposite\r\n" );
document.write( "in sign.\r\n" );
document.write( "\r\n" );
document.write( "Check by substituting -5 for k and solve:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " and  are numerically \r\n" );
document.write( "equal but opposite in sign.\r\n" );
document.write( "\r\n" );
document.write( "

\n" ); document.write( "--what should be the range of the value of k so that the equation
\n" ); document.write( " $\"+2x%5E2%2B3kx-9=0+\"$ will have real and unequal roots.
\n" ); document.write( "

\r\n" );
document.write( "That is when the discriminant is positive\r\n" );
document.write( "\r\n" );
document.write( "Find the discriminant \r\n" );
document.write( "\r\n" );
document.write( "\"Positive\" means the same as \"greater than 0\"\r\n" );
document.write( "\r\n" );
document.write( "So we set \r\n" );
document.write( "\r\n" );
document.write( "Divide through by 9\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since  is never negative the left side will always\r\n" );
document.write( "positive no matter what value of k we use, so all values of \r\n" );
document.write( "k will yield real and unequal roots.\r\n" );
document.write( "\r\n" );
document.write( "So \r\n" );
document.write( "\r\n" );
document.write( "

\n" ); document.write( "---what should be the value of k so that the equation $\"+x%5E2%2B%28k-2%29x%2B4=0+\"$
\n" ); document.write( "will have equal roots?
\n" ); document.write( "

\r\n" );
document.write( "Find the discriminant \r\n" );
document.write( "\r\n" );
document.write( "To have equal roots the discriminant must equal 0, so\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Divide thru by 4\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Using the , \r\n" );
document.write( "\r\n" );
document.write( "Using the , \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );