How do you find the discriminant of #x^2-12x+4=0#?

1 Answer
Dec 1, 2016

Answer:

#Delta = b^2-4ac#

Explanation:

#x^2-12x+4 = 0#

is in the form:

#ax^2+bx+c = 0#

with #a=1#, #b=-12# and #c=4#

It has discriminant #Delta# given by the formula:

#Delta = b^2-4ac = (-12)^2-4(1)(4) = 144-16 = 128 = 2*8^2#

Since #Delta > 0# this quadratic equation has two distinct Real roots, but since #Delta# is not a perfect square, those roots are irrational.

We can find the roots using the quadratic formula:

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

#color(white)(x) = (-b+-sqrt(Delta))/(2a)#

#color(white)(x) = (12+-sqrt(2*8^2))/2#

#color(white)(x) = (12+-8sqrt(2))/2#

#color(white)(x) = 6+-4sqrt(2)#