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

1 Answer
Alex Boroda
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.

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