# What is the discriminant of x^2-10x+25 and what does that mean?

Jul 17, 2015

Solve y = x^2 - 10x + 25 = 0

#### Explanation:

D = b^2 - 4ac = 100 - 100 = 0.
There is a double root at $x = - \frac{b}{2} a = \frac{10}{2} = 5$. The parabola is tangent to x-axis at x = 5.

Jul 17, 2015

The discriminant is zero so there is only one real (as opposed to imaginary) solution for $x$.

$x = 5$

#### Explanation:

${x}^{2} - 10 x + 25$ is a quadratic equation in the form of $a {x}^{2} + b x + c$, where $a = 1 , b = - 10 , \mathmr{and} c = 25$.

The discriminant of a quadratic equation is ${b}^{2} - 4 a c$.

Discriminant$= \left({\left(- 10\right)}^{2} - 4 \cdot 1 \cdot 25\right) = \left(100 - 100\right) = 0$

A discriminant of zero means there is only one real (as opposed to imaginary) solution for $x$.

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$ =

$x = \frac{- \left(- 10\right) \pm \sqrt{{\left(- 10\right)}^{2} - 4 \cdot 1 \cdot 25}}{2 \cdot 1}$ =

$x = \frac{10 \pm \sqrt{100 - 100}}{2}$ =

$x = \frac{10 \pm \sqrt{0}}{2}$ =

$x = \frac{10}{2}$ =

$x = 5$