Question 1095554
...the roots of the equation x^2+x+m=0 be real and unequal.
<pre>
So the dicriminant {{{b^2-4ac=(1)^2-4(1)m=1-4m}}}{{{"">""}}}{{{0}}}
                                         {{{-4m}}}{{{"">""}}}{{{-1}}}
                                           {{{m}}}{{{""<""}}}{{{1/4}}}
</pre>
Prove that the roots of the equation 2x^2+4(1+m)x+2m^2+3=0 are imaginary. where m is real.
<pre> 
{{{2x^2+4(1+m)x+2m^2+3}}}{{{""=""}}}{{{0}}}

We have to prove that the discriminant of that is negative:

{{{discriminant}}}{{{""=""}}}{{{b^2-4ac}}}{{{""=""}}}{{{(4(1+m)^"")^2-4(2)(2m^2+3)}}}{{{""=""}}}

{{{16(1+m)^2 - 8(2 m^2 + 3)}}}{{{""=""}}}{{{16(1+2m+m^2)-16m^2-24}}}{{{""=""}}}

{{{16+32m+16m^2-16m^2-24}}}{{{""=""}}}{{{32m-8}}}

Since {{{m}}}{{{""<""}}}{{{1/4}}}
      {{{32m}}}{{{""<""}}}{{{8}}}
      {{{32m-8}}}{{{""<""}}}{{{8-8}}}
      {{{32m-8}}}{{{""<""}}}{{{0}}}

Proved.

Edwin</pre>