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

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Answer 1 · 2015-07-17T04:16:25

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

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

Answer 2 · 2015-07-17T04:46:35

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

$x=5$

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

The discriminant of a quadratic equation is $b^2-4ac$ .

Discriminant $=((-10)^2-4*1*25)=(100-100)=0$

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

$x=(-b+-sqrt(b^2-4ac))/(2a)$ =

$x=(-(-10)+-sqrt((-10)^2-4*1*25))/(2*1)$ =

$x=(10+-sqrt(100-100))/2$ =

$x=(10+-sqrt0)/2$ =

$x=10/2$ =

$x=5$

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