# How do you find value of discriminant then describe number and type of solutions for x^2 - 16x + 64 = 0?

Jan 4, 2017

Discriminant value is 0. The solution is that both the roots would be equal to 8

#### Explanation:

Solution of a general quadratic equation of the form $a {x}^{2} + b x + c = 0$ is $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$ .

The expression inside the radical sign is called the Discriminant. There are two solutions (called roots) one each with a + and - sign in front of the radical. There are three possibilities of the Discriminant being <0, >0 or =0. Accordingly, if the Discriminant is <0, the roots are not real, they are imaginary. Secondly, if the Discriminant is >0, the roots are real and distinct. Lastly if the Discriminant =0, both the roots are equal.

In the present case, comparing the coefficients with the general equation, a=1, b= -16 and c=64. Thus the Discriminant would be ${\left(- 16\right)}^{2} - 4 \left(1\right) \left(64\right)$ = 0. Hence the solution would be both the roots being equal to 8