What is the discriminant of #2x^2 = 4x - 7# and what does that mean?

1 Answer
May 30, 2018

Answer:

In the equation #ax^2+bx+c=0#, the discriminant is #b^2-4ac#

Explanation:

By completing the square it is possible to see that the solutions of the equation:

#ax^2+bx+c=0#

are of the form:

#x_1#=#(-b + sqrt(b^2-4ac))/(2a) # and

#x_2#=#(-b - sqrt(b^2-4ac))/(2a) #

So, to have solutions in the real numbers (as opposed to complex numbers), the square root #sqrt(b^2-4ac# must exist as a real number, and so we need #b^2-4ac>=0#.

In summary, to have real solutions, the discriminant #b^2-4ac# of the equation must satisfy #b^2-4ac>=0#