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

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Answer 1 · 2015-05-17T23:14:35

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

$x_{1, 2}$ $x_(1,2)$ = $(- b +- sqrt Delta) / (2 a)$ , 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.

How to use the discriminant to find out what type of solutions the equation has for x^2-4x+10=0x2−4x+10=0x^2-4x+10=0?