document.write( "Question 335714: Determine the nature of the solution of the equation. 7t^2-8t=0
\n" ); document.write( "A) 2 real solutions
\n" ); document.write( "B) 2 imaginary solutions
\n" ); document.write( "C) 1 real solution \n" ); document.write( "

Algebra.Com's Answer #240745 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For any quadratic polynomial equation of the form:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Find the Discriminant,

and evaluate the nature of the roots as follows:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "No calculation quick look: If the signs on

and

are opposite, then

0\"> guaranteed.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

0 \ \ \Rightarrow\ \\"> Two real and unequal roots. If

is a perfect square, the quadratic factors over

.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

A conjugate pair of complex roots of the form

where

is the imaginary number defined by

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You have to put your quadratic into standard form and then you can see that a = 7, b = -8, and c = 0.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "John
\n" ); document.write( "

\n" ); document.write( "My calculator said it, I believe it, that settles it
\n" ); document.write( "

\n" ); document.write( " \n" ); document.write( "

\n" );