SOLUTION: I am having a tough time with these problems on this one I must use the discriminate to determine the number of solutions of the quadratic equation and whether the solutions are re

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I am having a tough time with these problems on this one I must use the discriminate to determine the number of solutions of the quadratic equation and whether the solutions are re      Log On


   

Question 235836: I am having a tough time with these problems on this one I must use the discriminate to determine the number of solutions of the quadratic equation and whether the solutions are real or complex. It is not necessary to find the roots just determine the number of types of solutions.
m^2 + m + 1 = 0
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
graph+%28600%2C600%2C-10%2C10%2C-10%2C10%2Cx%5E2+%2B+x+%2B+1%29

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.