Question 110906
Calculate the discriminant of:
{{{x^2+x+3 = 0}}}
The discriminant of a quadratic equation is the quantity: {{{b^2-4ac}}} (the number under the square root sign in the general form of the equation {{{x =(-b+-sqrt(b^2-4ac))/2a}}}
In your equation, you can see that a = a, b = 1, and c = 3, making the appropriate substitutions, we get:
{{{1^2-4(1)(3) = 1 - 12}}} = {{{-11}}}
When you see a negative number under the radical (square root sign), you know that the solutions of this quadratic will be complex roots.
This means that the graph of the equation (a parabola) does not intercept the x-axis at all.
Take a look at the graph to confirm this:
{{{graph(600,400,-5,5,-2,8,x^2+x+3)}}}