How to use the discriminant to find out what type of solutions the equation has for x^2-4x+10=0?

1 Answer
May 17, 2015

The general formula for the solutions of a quadratic equation a x^2 + b x + c is:

x_(1,2) = (- b +- sqrt Delta) / (2 a), where the discriminant Delta = b^2 - 4 a c.

We calculate the value of the discriminant for our particular equation
(x^2 - 4 x + 10):

Delta = 16 - 4 * 1 * 10 = - 22

As the discriminant Delta<0, our equation does not have solutions in the set of real numbers.