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#