Question 369077
{{{b^2-4ac}}} is called the discriminant. Its value will tell you how many roots of what type there are for a quadratic equation:<ul><li>{{{b^2-4ac > 0}}} means that there are two real roots.</li><li>{{{b^2-4ac = 0}}} means that there are one real root.</li><li>{{{b^2-4ac < 0}}} means that there are two complex roots. And if b = 0 then the complex roots are imaginary roots (i.e. the real part of the complex number will be zero).</li></ul>
The a, b and c for the discriminant come from the general form for quadratic equations: {{{ax^2 + bx + c = 0}}}. Looking at your equation, a = 2, b = -3 and c = c. This makes the discriminant:
{{{(-3)^2 -4(2)(c)}}}
which simplifies as follows:
{{{9 - 4(2)c}}}
{{{9 - 8c}}}
If we want complex roots then we want
{{{9 - 8c < 0}}}
Solving this I'll start by subtracting 9 from each side:
{{{-8c < -9}}}
Then dividing by -8. (Remember that whenever an inequaity is multiplied or divided by any negative number, like we are doing now, the inequality symbol must be reversed! This is why we have a "greater than" all of a sudden.)
{{{c > 9/8}}}<br>
NOTE: Since your b is not zero, there is no way to get imaginary roots.