Question 648818
The discriminant is the part of the quadratic formula that is inside the square root. That would be:

{{{b^2 - 4ac}}}




1.   {{{2x^2 + 5x + 5 = 0}}}


In this case, {{{b^2 - 4ac}}} comes to:

{{{25 - 4(2)(5)}}}

{{{25 - 80}}}

{{{-55}}}........

No Real Solutions-it has two imaginary solutions (reason: negative discriminant

{{{b^2 -4ac < 0}}})


2    {{{3z^2 + z - 1 = 0}}}

In this case, {{{b^2 - 4ac}}} comes to:

{{{1 - 4(3)(-1)}}}

{{{1 + 12}}}

{{{13}}}.......

Answer: Two Real Irrational Solutions (reason: {{{13}}} is positive, but not a perfect square)


3    {{{m^2 + m + 1 = 0}}}


In this case, {{{b^2 - 4ac}}} comes to:

{{{1 - 4(1)(1)}}}

{{{1 -4}}}

{{{-3}}}.......

No Real Solutions-it has two imaginary solutions (reason: negative discriminant

{{{b^2 - 4ac<0}}})