Question 235836
{{{graph (600,600,-10,10,-10,10,x^2 + x + 1)}}}


If you look at the graph, this equation should not have a solution.


The discriminant is equal b^2 - 4ac


The general form of a quadratic equation is:


ax^2 + bx + c


Your equation is:


m^2 + m + 1


Replace your "m" with "x" to get:


x^2 + x + 1


That makes your:


a = 1
b = 1 
c = 1


a is the coefficient of the x^2 term.
b is the coefficient of the x term.
c is the constant term.


b^2 - 4ac becomes:


1^2 - 4*1*1 which becomes -3


A negative discriminant means your quadratic equation has no roots.


The quadratic formula used to solve quadratic equations is:


-b +/- sqrt(b^2-4ac) / 2a


Your discriminant of b^2-4ac is under the square root sign.


square root of negative 3 gives you an imaginary number which is not real.


Since the roots of a quadratic equation are the "real" values of x when y = 0, this equation has no roots.


The graph confirms that since the graph of the equation never crosses the x-axis.