How do you find the value of the discriminant and determine the nature of the roots #x^2 + 9 = 6x#?

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Answer 1 · 2016-07-12T09:41:23

#Delta=0#

The given quadr. eqn. has two equal roots.

The discriminant #Delta# of a Quadratic Eqn. #: ax^2+bx+c=0# is given by,

#Delta=b^2-4ac#.

The quadr. eqn. given to us is #:x^2+9=6x#
#=>x^2-6x+9=0.#

Therefore, #a=1, b=-6, c=9#
# rArr Delta=(-6)^2-4*1*9=36-36=0#

# rArr# The given quadr. eqn. has two equal roots.

Answer 2 · 2016-07-12T14:23:09

double-root at x = 3

y = x^2 - 6x + 9 = (x - 3)^2
There is a double-root at x = 3. The parabola is tangent to x-axis
at x = 3. Vertex (3, 0)