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

1 Answer
George C.
Dec 1, 2016

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)

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