# How do you use the discriminant to determine the nature of the solutions given y = x^2 + 25– 10x?

The roots are real and identical because, discriminant $D = 0$
The roots are ${x}_{1} = \frac{5}{2}$ and ${x}_{2} = \frac{5}{2}$

#### Explanation:

The given equation is

$y = {x}^{2} - 10 x + 25$

and $a = 1$ and $b = - 10$ and $c = 25$

The discriminant

$D = \sqrt{{b}^{2} - 4 a c}$

$D = \sqrt{{\left(- 10\right)}^{2} - 4 \left(1\right) \left(25\right)}$

$D = \sqrt{100 - 100}$

$D = 0$

God bless....I hope the explanation is useful.